Question

A test consists of 20 questions, and students are asked to only answer 15 of them. In how many different ways can they choose 15 questions?

Answer 1

So to find how many ways to choose some number of things from another number
you do the permutation of them only if the order doesn't mattert:
\[P(20,15)\]
\[P(n,k)=\frac{ n! }{ k!(n-k!) }\]
So do:
\[\frac{ 20! }{ 15!(20-15!) }\]
Simplify:\[\frac{ 20! }{15!* 5! }\]
So the answer is 20!/15!*5!
Whatever that is just type it in on google or a calculator :

Answer 2

it should give you:
15504 ways to arrange the questions and do them in any order you want

Answer 3

btw \[P(n,k) \] in my answer up there should be:\[\left(\begin{matrix}n \\ k\end{matrix}\right)\]

Answer 4

\(20\choose 15\)?