Question

How many ways are there to select 7 countries in the united nations to serve on a council if 1 is selected from a block of 56, 3 are selected from a block of 63 and 3 are selected from the remaining 70 countries?

Answer 1

$56\cdot63C3\cdot70C3=\\\\ 56\cdot\dfrac{63!}{3!60!}\cdot\dfrac{70!}{3!67!}=\\\\ 56\cdot\dfrac{61\cdot62\cdot63}{2\cdot3}\cdot\dfrac{68\cdot69\cdot70}{2\cdot3}=\\\\ 121,731,687,840$