Question

The Senate in a certain state is comprised of 6060 ​Republicans, 3838 ​Democrats, and 22 IndependentsIndependents. How many committees can be formed if each committee must have 33 Republicans and 22 ​Democrats?

Answer 1

There can be 24056660 committees.

Explanation:

The Senate in a certain state is comprised of 60 ​Republicans, 38 ​Democrats, and 22 Independents.

Number of ways to pick 3 Republicans : 60C3 =
`(60!)/(3!(60-3)!)` = 34220

Number of ways to pick 2 ​Democrats : 38C2 =
`(38!)/(2!(38-2)!)`

= 703

And total number of committees formed =
`34220*703=24056660`