Question

N a second grade class containing 12 girls and 11 boys, 2 students are selected at random to give out the math papers. what is the probability that both are girls?

Answer 1

$\displaystyle |\Omega|=\binom{23}{2}=\dfrac{23!}{2!21!}=\dfrac{22\cdot23}{2}=253\\ |A|=\binom{12}{2}=\dfrac{12!}{2!10!}=\dfrac{11\cdot12}{2}=66\\\\ P(A)=\dfrac{66}{253}=\dfrac{6}{23}$