Question

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

Answer 1

Total boy = 25

Total girl = 10

Party of 8 to be made from 25 boys and 10 girls, selecting 5 boys and 3 girls

${\Rightarrow }^{25}{C}_5$ and ${}^{10}{C}_3$

${}^{25}{C}_5{\times }^{10}{C}_3$

Now, ${}^{25}{C}_5=\frac{n!}{r!(n-r)!}$

$\Rightarrow \frac{25!}{5!20!}\times \frac{10}{3!7!}$

$\Rightarrow \frac{25\times 24\times 23\times 22\times 21\times 10\times 9\times 8}{5\times 4\times 3\times 2\times 3\times 2}$

$=6375600$