Question

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)

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 $^{n-k+1}C_k$

$= \begin {pmatrix} ^{n-k+1}_{k} \end {pmatrix}$

where:

n = 26

k = 5

$^{n-k+1}C_k= \begin {pmatrix} ^{26-5+1}_{5} \end {pmatrix}$

$^{n-k+1}C_k= \begin {pmatrix} ^{22}_{5} \end {pmatrix}$

$^{n-k+1}C_k= \dfrac{22!}{5!(22-5)!}$

$^{n-k+1}C_k= \dfrac{22!}{5!(17)!}$

$\mathbf{^{n-k+1}C_k=26334}$

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