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

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`

`=(20!)/(15!5!)`

`=15504`