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

`\frac{\displaystyle\binom{8}{2}}{\displaystyle\binom{12}{2}}=\\\\ ((8!)/(2!6!))/((12!)/(2!10!))=\\\\\ (8!)/(2!6!)\cdot(2!10!)/(12!)=\\\\ (7\cdot8)/(2)\cdot(2)/(11\cdot12)=\\\\ (7\cdot4)/(11\cdot3)=\\\\ (28)/(33)`