Question

the number of combinations of five objects taken two at a time is?

Answer 1

One would assume for your question that the order in which these objects are picked is irrelevant. Therefore, we can use a function from combinatorics called the combination, where the number of combinations choosing p objects from a set of n objects is equal to nc_q=n!/((n−q)!q!). In this case, that would be equal to

 (5!)/((5−2)!2!)

=120/(3!2!)

=120/(6*2)

10

Therefore there are 10 combinations of 5 objects taken two at a time.