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

$^nC_r=\dfrac{n!}{r!(n-r)!}$

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

$^{100}C_6=\dfrac{100!}{6!(100-6)!}$

$^{100}C_6=\dfrac{100\times 99\times 98\times 97\times 96\times 95\times 94!}{6\times 5\times 4\times 3\times 2\times 1\times 94!}$

$^{100}C_6=\dfrac{100\times 99\times 98\times 97\times 96\times 95}{6\times 5\times 4\times 3\times 2\times 1}$

$^{100}C_6=1192052400$

Therefore, the total number of ways to form a committee is $^{100}C_6$, i.e., equal to $1192052400$.