Question

In how many ways can 7 different shirts hang on the rack if they all must face the same way? 7
210
5040
There are too many ways to count

Answer 1

@iPwnBunnies

Answer 2

@Abhisar

Answer 3

The number of permutations of ordering the shirts is 7!
Each of these permutations would have 2^7 ways of arranging the shirts if each shirt was allowed to face in one of two ways. In this case there would be a total of 7! * 2^7 ways of arranging the shirts. However only one of the 2^7 ways of facing the shirts is allowed for each permutation of ordering the shirts. Therefore there are 7! ways of arranging the shirts if they all must face the same way.

Answer 4

\[\frac{7! \times 2^{7}}{2^{7}}=7!\]