How many ways are there to select 8 countries in the United

How many ways are there to select 8 countries in the United Nations to serve on a council if 2 is selected from a block of 52, 1 are selected from a block of 63 and 5 are selected from the remaining 74 countries?

Solution

2 are selected from a block of 52 Means : 52C2 ways

1 are selected from a block of 63 means : 65C1 ways

5 are selected from remaining 73 countries : 73C5 ways

Total number of Ways =  52C2 ways * 65C1 ways *73C5 ways

= (52 * 51 / 2*1 ) * ( 65 /1 ) * ( 73 * 72 * 71 * 70 * 69 / 5 *4 *3 *2 *1)

= 1294602587460