Answer:
252.
Step-by-step explanation:
Order is not important because answering problem 1,2,3,4 and 5 is the same as answering problems 4,3,5,2 and 1. Since the order is not important, we use combination. The formula for taking r things from n possible ones with no order is expressed by.
\frac{n!}{n!(n-r)!}
n!(n−r)!
n!
We have 5 items to choose from 10 possible problems, so r = 5, n = 10. Substituting it to the formula and simplifying gives us:
\begin{gathered}=\frac{10!}{5!(10-5)!}\\\\=\frac{10!}{5!5!}\\ \\=\frac{10*9*8*7*6*5!}{5*4*3*2*1*5!}\\ \\=3*2*7*6\\\\=252\end{gathered}
=
5!(10−5)!
10!
=
5!5!
10!
=
5∗4∗3∗2∗1∗5!
10∗9∗8∗7∗6∗5!
=3∗2∗7∗6
=252
There are 252 ways to select 5 problems from 10 possible problems.
