Question

"A TV show has 24 episodes. Due to the lack of time, you can only watch 5 of them. However, in order to get a gist of what the show is about, you do not want to watch any two consecutive episodes. How many selections of 5 episodes are there with no two consecutive episodes chosen?"

Answer 1

Answer:15504

Step-by-step explanation:

We know to select any r no of non-consecutive  element for n consecutive elements is given by

$^{n-k+1}C_k i.e. \left ( ^{n-k+1}_k \right )$

Here n=24 and r=5

Therefore no of ways$=^{24-5+1}C_5$

$=^{20}C_5$

$=\frac{20!}{15!5!}$

$=15504$