Question

A test consist of 20 questions, but you are told to answer only 15. in how many different ways can you choose the 15 questions?

Answer 1

`((20),(15))=15504`

Explanation:

We don't care in what order we do the questions, and so this is a combination question:

`C_(n,k)=((n),(k))=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

and so we have:

`((20),(15))=15504`

If, however, you don't have a copy of Pascal's Triangle as your computer's background, we can work this the long way:

`(20!)/((15!)(5!))=(20xx19xx18xx17xx16)/120=15504`