Question

a class contains 30 children, 18 girls and 12 boys. Four complimentary tickets are distributed at random to the children in the class. what is the probability that 2 boys and 2 girls got the ticket

Answer 1

There are \[\left(\begin{matrix}30 \\ 4\end{matrix}\right)\] ways of ditributing 4 tickets to 30 children

There are
\[\left(\begin{matrix}18 \\ 2\end{matrix}\right)\]

ways of distributing 2 tickets to 18 girls and

\[\left(\begin{matrix}12 \\ 2\end{matrix}\right)\]

ways of distributing 2 tickets to 12 boys

so the probability for 2 girls and 2 boys getting a ticket is

\[\left(\begin{matrix}18 \\ 2\end{matrix}\right)\left(\begin{matrix}12 \\ 2\end{matrix}\right)/\left(\begin{matrix}30 \\ 4\end{matrix}\right)\]

I'll let you work out the combinatorial arithmetic

Answer 2

@alekos thanks