Question

How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?

Answer 1

Clearly, out of the 25 boys and 10 girls, 5 boys and 3 girls will be chosen.

Then, different boat parties of 8 = ${}^{25}{C}_5{\times }^{10}{C}_3$

$$\begin{gathered} =\frac{25!}{5!20!}\times \frac{10!}{3!7!} \\ =\frac{25\times 24\times 23\times 22\times 21}{5\times 4\times 3\times 2\times 1}\times \frac{10\times 9\times 8}{3\times 2\times 1} \\ =6375600 \end{gathered}$$