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

there are 5 ways to choose the matching pair
then once the matching pair is chosen, you have 8 other shoes to choose from
finally you have 6 shoes to choose from (because you cannot choose the match to the second shoe) so it is \(5\times 8\times 6\) by the counting principle, except that you have divide by 2 because the two odd shoes can be chosen in any order
to i believe your answer is 120

Answer 2

sounds good to me anyway

Answer 3

hello u there