is the number of ways of choosing a group of 5 from 10 available.
Taking one of these groups of 5, there will be 5 remaining.
is the number of ways to choose 3 from the remaining 5
(the 2 left over will always be unique to this 3).
Hence any selection of 5 from 10 can be matched with any one of these groups of 3 and 2.
Since there are groups of 5 in total,
we count the number of group matches by multiplying the number
of groups of 5 by the number of groups of 3.