How many permutations of the 26 letters of the English alphabet do not contain any of the strings fish, rat, or bird

Answers

Answer 1

The number of permutations of the 26 letters of the English alphabet that do not contain any of the strings fish, rat, or bird is 402619359782336797900800000

Let

[tex]\mathcal{E}=\{\text{All lowercase letters of the English Alphabet}\}\\\\B=\overline{\{b,i,r,d\}} \cup \{bird\}\\\\F=\overline{\{f,i,s,h\}} \cup \{fish\}\\\\R=\overline{\{r,a,t\}} \cup \{rat\}\\\\FR=\overline{\{f,i,s,h,r,a,t\}} \cup \{fish,rat\}[/tex]

Then

[tex]Perm(\mathcal{E})=\{\text{All orderings of all the elements of } \mathcal{E}\}\\\\Perm(B)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing bird}\}\\\\Perm(F)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing fish}\}\\\\Perm(R)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing rat}\}\\\\Perm(FR)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing both fish and rat}\}\\[/tex]

Note that since

[tex]F \cap R=\varnothing[/tex], [tex]Perm(F)\cap Perm(R)\ne \varnothing[/tex]

But since

[tex]B \cap R \ne \varnothing[/tex], [tex]Perm(B)\cap Perm(R)= \varnothing[/tex]

and

[tex]B \cap F \ne \varnothing[/tex] , [tex]Perm(B)\cap Perm(F)= \varnothing[/tex]

Since

[tex]|\mathcal{E} |=26 \text{, then, } |Perm(\mathcal{E})|=26! \\\\|B|=26-4+1=23 \text{, then, } |Perm(B)|=23!\\\\|F|=26-4+1=23 \text{, then, } |Perm(F)|=23!\\\\|R|=26-3+1=24 \text{, then, } |Perm(R)|=24!\\\\|FR|=26-7+2=21 \text{, then, } |Perm(FR)|=21!\\[/tex]

where [tex]|Perm(X)|=\text{number of possible permutations of the elements of X taking all at once}[/tex]

and

[tex]|Perm(F) \cup Perm(R)| = |Perm(F)| + |Perm(R)| - |Perm(FR)|\\= 23!+24!- 21! \text{ possibilities}[/tex]

What we are looking for is the number of permutations of the 26 letters of the alphabet that do  not contain the strings fish, rat or bird, or

[tex]|Perm(\mathcal{E})|-|Perm(B)|-|Perm(F)\cup Perm(R)|\\= 26!-23!-(23!+24!- 21!)\\= 402619359782336797900800000 \text{ possibilities}[/tex]

This link contains another solved problem on permutations:

https://brainly.com/question/7951365


Related Questions

simplify.
remove all perfect squares from inside the square roots. assume x and y are positive.
√8x^3y^2

Answers

Answer:

[tex]2xy\sqrt{2x}[/tex]

Step-by-step explanation:

Because this is a whole term in itself (no addition or subtraction), you can just directly find squares and factor them out. First, when looking at 8, you can factor out 4, to get 2 on the outside. Then, while looking at x cubed, you can factor out x squared, to get x on the outside, and when looking at y squared, you can just pull that outside itself, to get y. Now, we have one 2 and one x remaining, for a total of [tex]2xy\sqrt{2x}[/tex]

Use the graph to identify the following: end behavior. for a branlist

Answers

Answer:

the first option, increasing as x approaches infinity and decreasing as x approaches negative infinity

Step-by-step explanation:

help me pls I need help​

Answers

Answer:

parallel lines are two lines drawn next to each other without a intersection

Six children collect 45 pencils. 20% of the pencils need sharpening. How many pencils need
sharpening?

Answers

Answer:

9

Step-by-step explanation:

45*2/10=45*1/5=9

Answer:

9

Step-by-step explanation:

What are the solutions of y=x^2+5x-7

Answers

Answer:

You have two variables, and only one condition. It means you have infinite solutions of the form [tex](t; t^2+5t-7)[/tex]. Technically correct, probably not what you want to know.

If you wanted to know if and where the RHS crosses the x axis, the points are the solution to

[tex]x^2+5x-7= 0 \rightarrow x=\frac12(-5\pm\sqrt{25+28})\\x_1= \frac12(\sqrt{53}-5); x_2=-\frac12(\sqrt{53}+5)[/tex]

If you wanted the graph it's a parabola passing through the two points we just found, (0;-7), and with an axis of equation [tex]x=-\frac52[/tex].

The hanger image below represents a balanced equation.
27
V
Find the value of v that makes the equation true.
U =
I need the answer

Answers

Answer:

2x =3

The hanger image given in the figure represents balanced equation.

Then we have to write an equation to represent the image.

In balanced form left side = right side

x + x = 1 + 1 + 1

2x = 3

The value v is 9.

What is equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that is a structure showing a balanced hanger we need to find the value,

So we can say since the hanger is balanced therefore the weight both sides will be equal,

Therefore,

v + v + v = 27

3v = 27

v = 27

Hence the value v is 9.

Learn more about equation click;

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Help me with this please!!

Answers

Answer:

A=2/6 B=5/6

Step-by-step explanation:

I really hope this helps! (i love math!)

I NEED TO FINISH THESE BY NEXT WEEK

Answers

Answer:

Multiply both sides by 6:  4x - 42 = 5

Step-by-step explanation:

(2/3)x - 7 = (5/6)

Multiply both sides by 6:  

6*(2/3)x - 6*7 = 6*(5/6)

(12/3)x - 42 = 5

4x - 42 = 5

How do you solve
5x2 - 13x = 6
Using the ax2 +bx + c = 0 equation

Answers

I personally like the square method but I am lazy to draw this out (take too long)

5x²-13x-6 = (5x+2)(x-3)

x = -2/5 or 3

Double-check:

5x²-15x+2x-6  = 5x²-13x-6 √

the length of 2/3 a rope is (4u-5) inches Express the total length of the rope in terms of u

Answers

Answer:

6u - 15/2 inches

Step-by-step explanation:

(2/3)rope = 4u - 5

multiply both sides by 3/2

rope = 6u - 15/2

Given the complementary angle of y is 43º. Find the supplementary angle of y​

Answers

Step-by-step explanation:

complementary = adds up to 90 degrees.

supplementary = adds up to 180 degrees.

the complementary angle of y is 43 degrees.

so, y = 90 - 43 = 47 degrees.

the supplementary angle of y = 47 is

180 - 47 = 133 degrees

Hello!

Given the complementary angle of y is 43º.

90 - 43 => 47°

Find the supplementary angle of y​

180-43 => 137°

Which quadratic function shows a y-intercept of 4 and a maximum value of 5

Answers

Answer:

The 4th graph

Step-by-step explanation:

To have a maximum value, your parabola would have to open downwards. So the first 2 are wrong. Since your y-intercept is positive 4, your graph would have to touch the y axis at 4. The 3rd graph is wrong since it touches the y-axis at a negative point. The correct answer would be the 4th answer choice.

Dave throws sweets upwards at a speed of 8ms^-1 from a first floor window to his sister Carol who is standing at a second floor window 3m directly above Dave. Carol misses catching the sweet as it passes her hand on the way up, but catches it on the way down. Calculate the time it takes for Carol to catch the sweet after Dave has thrown it.

Answers

It would take [tex]1 second[/tex] for Carol to catch the sweet after Dave threw it.

Let

[tex]h=\text{maximum height}\\y=\text{distance from maximum height to Carol}\\t_h=\text{time taken to reach maximum height}\\t_y=\text{time taken to fall from maximum height to Carol}[/tex]

we want to calculate the value [tex]t_h+t_y[/tex]

First, we have to calculate [tex]t_h[/tex] using the formula

[tex]v=u+at[/tex]

using [tex]v=0[/tex], [tex]u=8[/tex], [tex]a=-10[/tex] (the sweets are decelerating due to gravity!)

[tex]0=8-(10)t_h\\10t_h=8\\t_h=\frac{8}{10}=0.8seconds[/tex]

To calculate [tex]t_y[/tex], first calculate [tex]h[/tex], then [tex]y[/tex]. Using the formula

[tex]h=ut+\frac{1}{2}at^2[/tex]

and the values [tex]u=8[/tex], [tex]t=t_h=0.8[/tex], [tex]a=-10[/tex] (again, the sweets are decelerating to get to maximum height)

[tex]h=(8)(0.8)+\frac{1}{2}(-10)(0.8)^2\\\\=6.4-3.2\\=3.2m[/tex]

since, Carol is standing [tex]3m[/tex] above Dave, we have the relationship

[tex]h=y+3[/tex]

so that

[tex]y=h-3\\=3.2-3\\=0.2m[/tex]

we can now calculate [tex]t_y[/tex];

[tex]y=ut_y+\frac{1}{2}gt_y^2[/tex]

taking [tex]y=0.2[/tex], [tex]u=0[/tex], [tex]g=10[/tex] (the sweets are falling, so they are now accelerating)

[tex]0.2=(0)t_y+\frac{1}{2}(10)t_y^2\\\\0.2=5t_y^2\\t_y^2=0.04\\\implies t_y=0.2seconds[/tex]

So it would take

[tex]t_h+t_y=0.8+0.2=1.0seconds[/tex]

for Carol to catch the sweet after Dave threw it from the first floor.

Learn more here: https://brainly.com/question/84352

the first term of an arithmetic sequence is a b and the second term is a c. What is the explicit formula to find the nth term of the sequence?

Answers

Step-by-step explanation:

every new term is created by adding a constant (I call here x) to the previous term.

a1 = b

a2 = c = a1 + x = b + x

a3 = a2 + x = a1 + 2x = b + 2x

so, we see

an = a1 + (n-1)x = b + (n-1)x

from a1 and a2 we know

c = b + x

x = c - b

so, ultimately we have

an = b + (n-1)(c-b)

The explicit formula to find the nth term of the sequence will be aₙ = cn - nb + 2b - c.

What is an arithmetic sequence?

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The first term of an arithmetic sequence is b and the second term is c.

a₁ = b

a₂ = c

Then the common difference is given as,

d = a₂ - a₁

d = c - b

Then the explicit formula to find the nth term of the sequence will be given as,

aₙ = b + (n - 1) × (c - b)

aₙ = b + cn - c - nb + b

aₙ = cn - nb + 2b - c

The explicit formula to find the nth term of the sequence will be aₙ = cn - nb + 2b - c.

More about the arithmetic sequence link is given below.

https://brainly.com/question/12373434

#SPJ5

on weekends a movie ticket costs $10.50. form an inequality and solve it to find the maximum number of tickets kate can buy with $205
STEP BY STEP EXPLANATION PLEASE

Answers

$10.50

10 Tickets would be $105.00

$105.00 - $10.50 = $94.50 so 9 Tickets would be $94.50

$105.00 + $94.50 = $199.50

$205.00 - $199.50 = $5.50 which isn't enough for another ticket.

10 Tickets + 9 Tickets = 19 Tickets.

If x = − 6, which number line shows the value of |x|?

Answers

Answer:

I would say the one that has the blue dot. bc, the absolute value of -6 is 6.

Answer:

The second one -6[------------]0 with 6 on top.

Step-by-step explanation:

What are the steps for solving -3/10 + 4/10

Answers

Answer:

1/10

Step-by-step explanation:

-3/10+4/10=4/10-3/10

                =1/10

Sale price = original price - rate of discount is the formula we used if original price and rate of discount are given. True or False, provide some explanation​

Answers

Answer:

I say true

Step-by-step explanation:

How to calculate discount and sale price:

Find the original price (for example $90 )

Get the discount percentage (for example 20% )

Calculate the savings: 20% of $90 = $18.

Subtract the savings from the original price to get the sale price: $90 - $18 = $72.

And You're all set!

Answer:

False

Step-by-step explanation:

Sale price = original price - rate of discount * original price

Rate of discount is a percent  so we need to multiply by the original price to get a a price so that all the units are the same.

Find the coordinates of the other endpoint when you are given the midpoint (point M) and one of the endpoints (point P).
P = (10, 6) and M = (-4, 8)

Answers

Answer:

 (-18, 10)

Step-by-step explanation:

If the other end point is Q, the midpoint is ...

  M = (P +Q)/2

  2M = P +Q

  Q = 2M -P = 2(-4, 8) -(10, 6) = (-8-10, 16-6)

  Q = (-18, 10)

The other end point is (-18, 10).

Here’s the full picture only 44, 45, 46, and 47

Answers

Answer:

m∠6 = 115; m∠5 = 115; m∠1 =  130; m∠4 = 65

Step-by-step explanation:

44.  m∠6 = 180 - 65 = 115

45. m∠5 = 180 - 65 =115

46. m∠1 = 180 - 50 = 130

47. m∠4 = 180 - (50+65) = 180 - 115 = 65

Answer:

the person below is correct

Step-by-step explanation:

hope it helped have an amazing night :)❤

Will give brainliest!

Answers

Answer:

D. 5/4

Step-by-step explanation:

Reciprocal is flipping that number around

Which of the following is a perfect square trinomial?
A. x²-6x+9
B. 4x²-20x-25
C. 4x²+20xy+9y2
D. 9a²-6a²bc+a²b²c²​

Answers

Make an educated guess, as A would be a great guess. Lol

A cylindrical water tank has a diameter of 4 m and a height of 3 m, while a water tank shaped like a rectangular prism has a length of 7 m, a width of 2 meters and a height of 2 meters. Which of the two tanks can hold more water? By how many cubic meters​

Answers

The 1st one can vary more by 12 cubic meters

7 is 75% of what number?

Answers

Answer:

9 1/3

Step-by-step explanation:

7 - 75%

x - 100%

[tex]\frac{7 * 100}{75} = 9\frac{1}{3}[/tex]

Answer:

7 is 75% of What Number? - 7 is 75% of 9.33. 100% of 9.33 is 9.33, therefore 75 percent of 9.33 equals 7.

Step-by-step explanation:

7 is 75% of What Number? - 7 is 75% of 9.33. 100% of 9.33 is 9.33, therefore 75 percent of 9.33 equals 7.

yefgfsugsuifdsgsdhgsfjhdgjdhgskhb

Write the prime factorization of 315.

315 =


(TRY TO ANSWER THIS WHILE UR AT IT PLS?

Answers

Answer:

315 = 3^2 × 5^1 × 7^1

Step-by-step explanation:

Jane bought 8 packs of red bouncy balls, 4 packs of yellow bouncy balls, and 4 packs of green bouncy balls. There were 8 bouncy balls in each package. How many bouncy balls did Jane buy in all?

Answer for 87 points <3

Answers

Answer:

128

Step-by-step explanation:

8×8 = 64

8×4 = 32

8×4 = 32

64 + 32 + 32 = 128

Drake bought a $110,000 life insurance policy at $12.95 for a 20 year term.
What will he pay over 20 years for the premium?

Answers

Drake will pay $28,490 over 20 years for the premium.

Data and Calculations:

Life insurance policy = $110,000

Insurance term = 20 years

Premium rate = $12.95 per $1,000

Total premium per year = $1,424.50 ($12.95 x $110,000/$1,000)

Total premium for 20 years = $28,490 ($12.95 x $110,000/$1,000 x 20)

Thus, Drake will pay a total premium of $28,490 for 20 years.

Learn more: https://brainly.com/question/3164505

A chessboard has 8 rows of squares with 8 squares in each row . Two players each put 16 chess pieces on the board , with each piece on its own square. How many squares are empty now? Explain your answer.

Answers

Answer:

40

Step-by-step explanation:

8x8 if 56 - 16 = 40

13- pls help with this pre-algebra problem is urgent

Answers

Answer:

What else is in the equation?

Step-by-step explanation:

Also, i think the - should be right here>-13 instead of it being here 13-<

Find the perimeter. Simplify your answer.

Answers

Answer:

The perimeter of the Parallelogram is 20z + 16

Step-by-step explanation:

For a Parallelogram

Perimeter = sum of all sides

P = (7z + 3) + (7z + 3) + (3z + 5) + (3z + 5)

P = 7z + 7z + 3z + 3z + 3 + 3 + 5 + 5

P = 20z + 16

Thus, The perimeter of the Parallelogram is 20z + 16

-TheUnknownScientist 72

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