Question

How many ways are there to select 15 countries in the United Nations to serve on a council if 4 are selected from a block of 35, 5 are selected from a block of 40, and the others are selected from the remaining 55 countries?

Answer 1

The order does not matter

$$N=\dbinom{35}{4}\dbinom{40}{5}\dbinom{55}{15-4-5}$$

$$=\dfrac{35!}{4!(35-4)!}\cdot \dfrac{40!}{5!(40-5)!}\cdot \dfrac{55!}{6!(55-6)!}$$

$$=52360\cdot 658008\cdot28989675$$

$$=998,789,937,209,064,000(ways)$$