Question

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.

Answer 1

10*8*6*3

Answer 2

=1440

Answer 3

start with 10 shoes which is 5 piars
select 1 shoe, you have 10 choices
select 2nd shoe, you have 9-1 choices since you can't match the first shoe
select 3rd shoe, you have 7-1 choices since you can't match the first or second shoe
select the 4th show, you have 3 choices, which is the matching pair of one of your first 3 choices