Question

What is 7P2?

Answer 1

`"_7P_2=42`

Explanation:

Recall the formula for permutations:
`"_nP_r=(n!)/((n-r)!)`

Therefore:
`"_7P_2=(7!)/((7-2)!)`

This calculation can be performed by hand without too much difficulty:
`"_7P_2=(7!)/((7-2)!)`
`=(7!)/(5!)`
`=(7*6*5!)/(5!)`
`->(7*6*cancel(5!))/cancel(5!)`
`=7*6=42`

This means that there are `42` ways to choose `2` objects from a set of `7` if order is important (i.e. 12 and 21 are two different ways to choose).