A club has 45 members and its membership committee has 7 members. How many different membership committees are possible?
I keep getting 1.6336632e10, but I know its not right somehow
The order of selection in a committee is usually not important.
So we are "choosing" groups of 7 from 45
which is C(45,7)
or 45!/(7!38!) = 453796620
To calculate the number of different membership committees possible, we need to use the concept of combinations.
In this case, we are selecting 7 members out of a total of 45 members. The order in which the members are selected doesn't matter, and each member can only be selected once.
The formula for calculating combinations is given by:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of items and r is the number of items to be selected.
Let's plug in the values:
C(45, 7) = 45! / (7! * (45-7)!)
To simplify this, we can use the factorial function:
n! = n * (n-1) * (n-2) * ... * 3 * 2 * 1
Using a calculator or a programming language that supports large numbers, we can evaluate this expression.
Calculating C(45, 7) = 45379620
Therefore, there are 45,379,620 different membership committees possible for the club.