A cupboard contains 55 pairs of shoes, each of a different style. How many ways are there to select 44 of the shoes from the cupboard so that the selection contains exactly one matching pair? Note that each pair of shoes consists of a distinguishable left and right foot.

1) General choice of shoes:

C (6,1) = choose the matching pair = 6 choices.

C (10,1) = 1 shoe from the other 10.

Now you cannot choose the mate of that one,

so you have 8 other shoes to choose from.

6 * 10 * 8 = 480 choices of "4 shoes".

But then we must divide by 2, because the last two shoes

could be chosen in either order.

That gives 240 choices