# What is 7P2?

Jul 17, 2016

"_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!)
$= 7 \cdot 6 = 42$

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).