A TV show has 26 episodes. Due to the lack of time, you can onlywatch 5 of them. However, in order to get a gist of what the showis about, you do not want to watch any two consecutive episodes.How many selections of 5 episodes are there with no two consecutiveepisodes chosen? Assuming that the order of selection is irrelevant.(Hint:this is a Stars and Bars problem)

Answers

Answer 1

Answer:

Step-by-step explanation:

Recall that: The number of combination to select any k consecutive element from n consecutive term is given by the equation [tex]^{n-k+1}C_k[/tex]

[tex]= \begin {pmatrix} ^{n-k+1}_{k} \end {pmatrix}[/tex]

where:

n = 26

k = 5

[tex]^{n-k+1}C_k= \begin {pmatrix} ^{26-5+1}_{5} \end {pmatrix}[/tex]

[tex]^{n-k+1}C_k= \begin {pmatrix} ^{22}_{5} \end {pmatrix}[/tex]

[tex]^{n-k+1}C_k= \dfrac{22!}{5!(22-5)!}[/tex]

[tex]^{n-k+1}C_k= \dfrac{22!}{5!(17)!}[/tex]

[tex]\mathbf{^{n-k+1}C_k=26334}[/tex]

Therefore, there are 26334 selection of 5 episodes with no two consecutive episodes chosen


Related Questions

Over the past several years, the owner of a boutique on Aspen Avenue has observed a pattern in the amount of revenue for the store. The revenue reaches a maximum of about $ 46000 in March and a minimum of about $ 28000 in September. Suppose the months are numbered 1 through 12, and write a function of the form ()=sin([−])+ f ( x ) = A sin ⁡ ( B [ x − C ] ) + D that models the boutique's revenue during the year, where x corresponds to the month. If needed, you can enter π =3.1416... as 'pi' in your answer. ()= f ( x ) =

Answers

Answer:

F(x) = [tex]9000 sin (\frac{\pi }{3} (x-3) + 37000[/tex]

Step-by-step explanation:

Revenue reached in March = $46000  ( Maximum )

Revenue reached in September = $28000 ( Minimum )

f(x)=Asin(B[x−C])+D

attached below is the detailed solution of the problem

attached below is the detailed solution

F(x) = [tex]9000 sin (\frac{\pi }{3} (x-3) + 37000[/tex]

point slope equation slope=8 point on line is (5,6)​

Answers

Answer:

c

Step-by-step explanation:

Answer:

y=8x-34

Step-by-step explanation:

sixteen people wore white socks. The ratio of those who wore white socks to those who wore black socks 1:2. How many people wore black socks?

Answers

Answer:

It should be 32.

Step-by-step explanation:

Change 3.5 decimal into a percent

Answers

Like out of 100? Then it would be 3.5%

The answer you're looking for is: 350%

(Tell me if i'm wrong please)


Find the length and width of a rectangle with maximum area that has a perimeter of 9P units.

Answers

Answer:

l = 9p/4 , l = 9p/4

Step-by-step explanation:

Given:

Perimeter = 9p

Find:

Length and width

Computation:

Assume;

Length = l

Perimeter = 2(l+b)

9p/2 = l+w

w = 9p/2 - l

Area = lb

Area = l(9p/2 - l)

Using differentiation

l = 9p/4

w = 9p/2 - l

w = 9p/2 - 9p/4

w = 9p/4

evaluate the function when x = 5
P(x) = -3 + 4x

Answers

Answer:

P(x) = 17

Step-by-step explanation:

P(5) = -3 + 4(5)     <- Substitute X

P(5) = -3 + 20       <- Multiply

P(5) = 17                <- Combine Like Terms

Answer:

P(5)=-3+4(5)

P(5)=-3+20

P(5)=17

-2[(-19 + - 5) + (3 - 7)] + -2 [(-12 - 2) -(4 - 6)]

Answers

Answer:

I got 80

Step-by-step explanation:

-2[-14+4]+2[-10-2]
-2-19+2-8
-2-21-8
11

Justin bought 12 souvenirs
during 6 days of vacation. How
many days will Justin have to
spend on vacation before he will
have bought a total of 20
souvenirs ?

Answers

Answer:

10

Step-by-step explanation:

10 days, because he got 2 souvenirs a day, so 20/2 = 10

Who likes sushi?!?!?!

Answers

Answer:

I do :)

Step-by-step explanation:

Lol I usually get the crunchy roll

I need help with this and can you explain how to do this?
3(2y + 3) + y

Answers

Answer: 7y + 9

Step-by-step explanation: First you will distribute 3(2y + 3). This means we will multiply 3 to the numbers in the parenthesis. 3 x 2y = 6y and 3 x 3 = 9. This is 6y + 9.

Now we have the y left over so combine like terms 6y + y and that is 7y.

Answer:

7y + 9.

Step-by-step explanation:

1. Expand by distributing terms.

3(2y + 3) + y

2. Collect like terms.

(6y + y) + 9.

3. Simplify.

7y + 9.

Hope this helps.

Have a good night ma´am/sir.

Be safe!

4x + xz + 8 - 4xz- 7z

Answers

Answer: if your trying to simplify it....

−3xz+4x−7z+8 <----- this is your answer

if your trying to factor...

4x−3xz+8−7z <------ is your answer

if Finding the exact value using trigonometric identities.

−3xz+4x−7z+8 <---- is your Answer

I don't know where your going with this....

Step-by-step explanation:

Let's simplify step-by-step.

4x+xz+8−4xz−7z

=4x+xz+8+−4xz+−7z

Combine Like Terms:

=4x+xz+8+−4xz+−7z

=(xz+−4xz)+(4x)+(−7z)+(8)

=−3xz+4x+−7z+8

Answer:

=−3xz+4x−7z+8

HELPPPPPPPPPP
A cafeteria sold 8 1/6 gallons of soda during lunchtime. 2 5/6 gallons were regular soda, and the rest was diet soda. How many gallons of diet soda were sold?

Write your answer as a fraction or as a whole or mixed number.

_________ gallons

Answers

Answer:

5 1/3 gallons

Step-by-step explanation:

Equation: 8 1/6 - 2 5/6

8-2=6

1/6-5/6= -4/6

6-4/6=5 2/6

Simplify:

5 1/3 gallons

Which expression represents a quadratic expression in complete factored form?


A. (x+4)(x-3)
B. (x-1)(3x-9)
C. (2x+4)(x+3)
D. (x-2) + (x+3)


ANSWER PLSSSSSSSSSSSSS, thanks.

Answers

Answer:

A. (x+4)(x-3)

Step-by-step explanation:

x+4=0 or x-3=0

x=-4 or x=3

Answer:

Have a great rest of your day :)

Step-by-step explanation:

James wants to buy a phone card for international calls when he travels to Paris this summer. He can buy a 200-
minute card for $10.50 or a 300-minute card for $18.25. Which card is cheaper to buy per minute? (2pts) Write the
number of minutes card on the answer line.

Answers

Answer:eoeould say 18.25 because for 300 minutes only for 18.25 is cheap.And yes the other one is cheaper but for the money but its only 200.Tell me would YOU want only 200 instead of 300 because 300 costs a lot more than 18.25 so that person must be getting it on sale lol HOPE THIS HELPS AND IS RIGHT!!!!! ;)

Step-by-step explanation:

NEED HELP WITH MATH! Will Give Brainliest! Image is below.

Answers

Answer:

2

Step-by-step explanation:

I need help please ​

Answers

Answer:

x=-4

Step-by-step explanation:

When the slope is undefined, we have a vertical line

A vertical line is of the form

x=

We have a point ( -4,2) so the x coordinate is -4

x=-4

Answer:

( -4,2)

Step-by-step explanation:

Which is greater 6/12 or 1/3

Answers

Answer:

1/3 is bigger

Step-by-step explanation:

6/12 might look bigger but its not

    PLEASE MARK AS BRAINLIEST

The sum of three numbers is 97. The third number is 2 times the second. The second number is 9 less than the first. What are the numbers?

Answers

Answer:

The numbers are 26.5, 53 and 17.5.

Step-by-step explanation:

97=x+(x-9)+2x

97+9=4x

106/4=4x/4

x= 26.5

x-9 = 17.5

2x= 53

Simplify. 32v2 the power of 4/ 8v to the power of 6

Answers

the answer is 4/v to the power of two

pls tell meeeeeeeeeeeeee

Answers

Girl you just have to divide 128 and 8

The expression 7(y-5)is equivalent to

Answers

7(y-5) = 7y-35

because 7(y) = 7y

and 7(-5) = -35

therefore 7y-35 is your answer

find the value of x ​

Answers

Answer:

141°

 

Step-by-step explanation:

  The angle given is 39°;

 

Since this problem deals with angles in a transversal, it is easy to solve.

Now;

       Angle given is a corresponding angle to the angle a;

  Corresponding angles are equal; so angle a  = 39°

Also,

   angle a is corresponding to angle b;

         angle b  = 39°

So, angle b and x are on a straight line;

           b  + x  = 180

                  x = 180 - 39  = 141°

 

free brainlyest if answer 9+10 the right way

Answers

Answer:

19

Step-by-step explanation:

literally if this is wrong i swear

Answer:

19

Step-by-step explanation:

someone help fast please

Answers

Answer:

c. supplementary angles

Step-by-step explanation:

Leah’s family took a 3-hour trip in a car. They left at 10:30 am. What time did Leah’s family arrive?

Answers

Answer:

1:30 Pm

Step-by-step explanation:

If the car ride was exactly 3 hours and they left and exactly 10:30 am then its would be 1:30pm because it goes 10:30 11:30 12:30 then 1:30

bernie spends three hours a day on homework. if the spends 3/4 of an hour on science, 3/4 of an hour on social studies, and 1/4 of an hour on english, how much time does bernie spend on math

Answers

3/4 of an hour is 45 minutes
1/4 of an hour is 15 minutes
3 hours is 180 minutes

3/4 + 3/4 = 90 minutes ( 45 + 44 )
90 + 15 = 105

180 - 105 = 75 minutes

Bernie will spend 75 minutes on math

Answer:

Step-by-step explanation:

Math = 3 - Science - social studies - english

Math = 3 - 3/4 - 3/4 - 1/4

Math = 3 - 1 3/4

Math = 3 - 1.75

Math = 1.25 or 1 1/4

(4.3 x 10^-3)(2 x 10^-2) in standard form

Answers

Answer:

8.6•10^-5 or 0.000086

Find the distance between each pair of points in the coordinate plane.
(3,-2) and (2,-1)​

Answers

Answer:

1.41

Step-by-step explanation:

Evaluate and reduce:
3
4
35 - -
F
Enter the number that belongs in the
green box.

Answers

Answer:

28

Step-by-step explanation:

35/5 ÷ -3/4

=7÷ (-3/4)

=7× (4/-3)

=(7×4)/-3

=- 28/3

the minus is already placed in the question, that makes the answer 28 without the minus

Describe how to plot point A(-6, 2) on a coordinate plane.

Answers

Answer:

Read the explanation

Step-by-step explanation:

Go to desmos (website) and open the Graphic Calculator (or you can use any graphic calculator) . Then in one of the text boxes on the side write A(-6,2) and it'll plot it. Or make a paper graph (Make sure the lines are spaced out correctly) and go to -6 on the x axis and 2 on the y axis, the point in which those 2 intecept is the plotted dot. Or print a graph and plot it there, both work.

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