Probability?

Question

How many ways are there to select 12 countries in the United Nations to serve on a council if 2 is selected from a block of 53, 1 are selected from a block of 64 and 9 are selected from the remaining 72 countries?

Answer 1

This is a combination, because the order in which the people are chosen does not matter. There are three combinations which you'll use:

 

Block of 53: 53 C 2 = 53!/[2!(53-2)!]

Block of 64: 64 C 1 = 64!/[1!(64-1)!]

Block of 72: 72 C 9 = 72!/[9!(72-9)!]

 

The final answer will be the multiple of the three combinations:

 

(53!/[2!(53-2)!]) x (64!/[1!(64-1)!]) x (72!/[9!(72-9)!])

 

53 C 2 = 1378
64 C 1 = 64
72 C 9 = 85113005120

When you multiply all those numbers together you should get 7.5 x 10^15