Alicia has 7 paintings and wishes to display 4 of them on her wall. In how many ways can she display them?

1 Answer
Alan N.
Feb 10, 2016

Assuming the order of the paintings on the wall matters then 4 of the 7 paintings can be displayed in 840 different ways.

Explanation:

The number of permutations of n items taken k at a time is given by:
#P(n,k) = {n!}/{(n-k)!}#

In this case Alicia has 7 paintings (n) and wishes to display 4 of them (k)

Therefore #P(7,4) = (7!)/[(7-4)!]#
#= (7.6.5.4.3.2.1) / (3.2.1) = 7.6.5.4#

# = 840#

Therefore Alicia can display 4 paintings from her total of 7 in 840 different ways.

Note: If the order of the paintings on the wall did not matter then the number of combinations would be given by:
#C(n,k) = {n!}/{(n-k)!k!# #= [P(n,k)] /(k!)#
Which in this case is #840/(4.3.2.1)# = #840/24# = #35#

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