step 1
Find out the total possible outcomes
Calculate 19C14
[tex]19C14=\frac{19!}{14!(19-14)!}=11,628[/tex]
step 2
Find out 10C6 (boy kittens)
[tex]10C6=\frac{10!}{6!(10-6)!}=210[/tex]
step 3
Find out 9C8 (girl kittens)
[tex]9C8=\frac{9!}{8!(9-8)!}=9[/tex]
step 4
Find out the probability that the director chooses 6 boys and 8 girls
[tex]P=\frac{(210)*(9)}{11,628}=0.163[/tex]
the answer is 0.163
