A company has $25$ employees.
a) A picture has to be taken of all of the employees for the new company website. How many possibilites are there to order the employees in a row.
b) 7 employees will be picked for a representative group photo. How many possibilites are there of the photo, if the rest of the employees return back to the row.
a) I think the answer is $25!$ resulting in a huge number.
b) Since we know the order here matters, I used the permuation formula $\frac{n!}{(n-r)!}=\frac{25!}{(25-7)!}=\frac{25!}{18!}=2422728000$
Are these valid solutions?
b) is a bit unclear in my opinion: in case we just want 7 out of 25, it is $\binom{25}{7}$. But if the order matters, we need to multiply the selection by $7!$, as you did.