Question

Someone please help me out please!!!!

Answer 1

Given:

A committee of 6 members is to be chose from the 100 members of the U.S. senate.

To find:

The number of ways to form a committee.

Solution:

We have,

Total number of members = 100

Number of members needs to selected of committee = 6

Number of ways to select r items from total n items is

`^nC_r=(n!)/(r!(n-r)!)`

Number of ways to select 6 members from total 100 members is

`^(100)C_6=(100!)/(6!(100-6)!)`

`^(100)C_6=(100* 99* 98* 97* 96* 95* 94!)/(6* 5* 4* 3* 2* 1* 94!)`

`^(100)C_6=(100* 99* 98* 97* 96* 95)/(6* 5* 4* 3* 2* 1)`

`^(100)C_6=1192052400`

Therefore, the total number of ways to form a committee is
`^(100)C_6`, i.e., equal to
`1192052400`.