Answer:
There are 44,186,943,000,000,000 different committees are possible from the 100 U.S. senators.
Step-by-step explanation:
The order is not important.
Suppose the committee had two members.
Senator A and Senator B would be the same committee as Senator B and Senator A.
So we use the combinations formula to solve this problem
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
U.S. Senate Committee has 14 members. Assuming party affiliation is not a factor in selection, how many different committees are possible from the 100 U.S. senators?
This is the number of combinations of 14 from 100. So
[tex]C_{100,14} = \frac{100!}{14!(86)!} = 44,186,943,000,000,000[/tex]
There are 44,186,943,000,000,000 different committees are possible from the 100 U.S. senators.
