Posted by Tom on Thursday, May 24, 2012 at 11:43pm.
Define
C(n,r)=n!/(r!(n-r)!)=n choose r
Sample space: C(13,5)=1287
ways to choose 0 boy
=Choose 5 girls out of 7 and 0 boy out of 6
=C(7,5)*C(6,0)=21
ways to choose 1 boy:
=C(7,4)*C(6,1)=210
ways to choose 2 boys:
=C(7,3)*C(6,2)=525
ways to choose 3 boys:
=C(7,2)*C(6,3)=420
ways to choose 4 boys:
=C(7,1)*C(6,4)=105
ways to choose 5 boys:
=C(7,0)*C(6,5)=6
If you add them all up, they will total 1287 as required.
Now make appropriate sums according to requirements and calculate probability.