Assume that there are 9 girls and 10 boys in the neighborhood club, and a team of 5 is to be selected.

Question

(1) How many different teams can be selected? 

(2) How many different teams can be selected if each team must contain exactly 2 girls and 3 boys? 

(3) How many different teams can be selected if each team must contain both boys and girls? 

Answer 1

So that these problems disappear...

a) 9 girls +10 boys = 19

choose 5 from 19 for team is

C(19,5)= 19*18*17*16*15/(5*4*3*2*1) = 11628

b) choose 2 girls from 9 and 3 boys from 10 = C(9,2) * C(10,3) = 36 * 120 = 4320

c) This would be all teams but those with all boys and all girls = C(19,5)- C(9,5)-C(10,5) =

11628 - 126 - 252 = 11250