Math Problem?

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 54, 2 are selected from a block of 62 and 4 are selected from the remaining 73 countries?

Answer 1

assuming blocks do not intersect

answer = (54 choose 1) * (62 choose 2) * (73 choose 4)

= (54 * 62 * 61 * 73 * 72 * 71 * 70) / (4 * 3 * 2 * 2)
= 111,143,941,020

Answer 2

54 ways to select 1 from 54
62C2 =62!/60!*2! = 1891 ways to select 2 from 62
73C4 = 73!/69!*4!= 1,088,430 ways to select 4 from 73
So multiply these together for your answer