Assume that there are 12 girls and 8
boys in the neighborhood club, and a team of 6 is
to be selected.
(1) How many different teams can be selected?
(2) How many different teams can be selected
if each team must contain exactly 4 girls and 2
boys?
(3) How many different teams can be selected
if each team must contain both boys and girls?

Question

Assume that there are 12 girls and 8
boys in the neighborhood club, and a team of 6 is
to be selected.
(1) How many different teams can be selected?
(2) How many different teams can be selected
if each team must contain exactly 4 girls and 2
boys?
(3) How many different teams can be selected
if each team must contain both boys and girls?

anonymous · Answer

(1)three different teams(2)three different teams(3)three different teams.

dumbcow · Answer

1)   20C6 = 38,760

2) 12C4 * 8C2 = 495*28 = 13,860

3) 20C6 - 12C6 -8C6 = 38,760 - 924 -28 = 37,808