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(63!)/(3!60!)\cdot(70!)/(3!67!)=\\\\ 56\cdot(61\cdot62\cdot63)/(2\cdot3)\cdot(68\cdot69\cdot70)/(2\cdot3)=\\\\ 121,731,687,840`