A cupboard contains 5 pairs of shoes, each of a different style. How many ways are there to select 4 of the shoes from the cupboard so that the selection contains exactly one matching pair? Note that each pair of shoes consists of distinguishable left and right foot.

Question

anonymous · Answer

Pair + RR + LL + RL broken down right?

anonymous · Answer

6 choices of matching pair.
Then
5 x 4 = 20 ways to choose a right shoe and a non-matching left
+
5c2 = 10 ways to choose two rights
+
5c2 = 10 ways to choose two lefts

Total = 6 * (20 + 20) = 6 * 40 = 240