Question

a family has 8 girls and 4 boys. A total of 2 children must be chosen to speak on behalf of the family at a local benefit. What is the probability that 2 girls and no boys are chosen? Using Combination and Permutation.

Answer 1

$\dfrac{\displaystyle\binom{8}{2}}{\displaystyle\binom{12}{2}}=\\\\ \dfrac{\dfrac{8!}{2!6!}}{\dfrac{12!}{2!10!}}=\\\\\ \dfrac{8!}{2!6!}\cdot\dfrac{2!10!}{12!}=\\\\ \dfrac{7\cdot8}{2}\cdot\dfrac{2}{11\cdot12}=\\\\ \dfrac{7\cdot4}{11\cdot3}=\\\\ \dfrac{28}{33}$