how many ways can 5 members of the 100 member US senate be chosen to be put on a committe?
100 choose 5, or
100!/(5!(100-5))!
=100*99*98*97*96/(1*2*3*4*5)
=75287520
To determine the number of ways 5 members can be chosen from a group of 100 members for a committee, you can use the concept of combinations.
The formula to calculate combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where:
- C(n, r) represents the number of combinations of n items taken r at a time.
- n! represents the factorial of n, which is the product of all positive integers from 1 to n.
- r! represents the factorial of r.
- (n - r)! represents the factorial of (n - r).
In this case, n = 100 (total members in the US Senate) and r = 5 (number of members to be chosen for the committee).
Plugging the values into the formula:
C(100, 5) = 100! / (5! * (100 - 5)!)
Calculating the factorials:
C(100, 5) = 100! / (5! * 95!)
Now, we need to calculate the factorials of 100 and 5:
100! = 100 * 99 * 98 * ... * 3 * 2 * 1
5! = 5 * 4 * 3 * 2 * 1
Simplifying the equation:
C(100, 5) = (100 * 99 * 98 * ... * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1 * (95 * 94 * ... * 3 * 2 * 1))
Canceling out the common terms:
C(100, 5) = (100 * 99 * 98 * ... * 96) / (5 * 4 * 3 * 2 * 1)
Calculating the values:
C(100, 5) = 75,287,520
Therefore, there are 75,287,520 different ways to choose 5 members from a 100-member US Senate to form a committee.