What is 7P2?

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1 Answer
Ken C.
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*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).

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