Question Number 102800 by bramlex last updated on 11/Jul/20

There are 14 boys and 10 girls in  a classroom. The teacher wants  to form a team of 5 students .  The team must have a least two  boys and two girls . Find the  number of ways the team can be  chosen.

Answered by bemath last updated on 11/Jul/20

case(1) 3boys &2 girls⇒C_3 ^(14)  ×C_2 ^(10)   =((14.13.12)/(3.2.1)) × ((10.9)/(2.1)) = 13680  (2)2boys &3 girls⇒C_2 ^(14) ×C_3 ^(10)  = ((14.13)/(2.1))×((10.9.8)/(3.2.1))  = 10920  totally = 13680+10920 =24600