Question

Find the value of the combination. From a committee consisting of 8 men and 5 women, a subcommittee is formed consisting of 4 men and 3 women. How many different subcommittees are possible?
80

700

1,716

Answer 1

Out of 8 men, 4 can be selected and lined up in (8 x 7 x 6 x 5) = 1,680 ways.
But within that number, each group of 4 appears in (4 x 3 x 2) = 24 orders.
So there are (1,680 / 24) = 70 different groups of men.

Out of 5 women, 3 can be selected and lined up in (5 x 4 x 3) = 60 ways.
But within that number, each group of 3 appears in (3 x 2) = 6 orders.
So there are (60 / 6) = 10 different groups of women.

Each different group of 70 men can be joined by any of the 10 groups
of women. So the total number of possible subcommittees is (70 x 10) = 700 .