How many ways can you set up a committee of 4 people from 10 people?
To determine the number of ways to set up a committee of 4 people from a group of 10 people, we can use the concept of combinations.
In this case, we need to calculate the number of combinations of 10 people taken 4 at a time. This can be calculated using the formula for combinations, which is:
C(n, r) = n! / (r! * (n-r)!)
where:
C(n, r) represents the number of combinations of n objects taken r at a time,
n! represents the factorial of n (i.e., n * (n-1) * (n-2) * ... * 3 * 2 * 1),
r! represents the factorial of r, and
(n-r)! represents the factorial of (n-r).
Plugging in the given values, we have:
C(10, 4) = 10! / (4! * (10-4)!)
= 10! / (4! * 6!)
To simplify this calculation, we can cancel out common terms in the numerators and denominators:
C(10, 4) = (10 * 9 * 8 * 7 * 6!) / (4! * 6!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
Performing the multiplication and division, we find:
C(10, 4) = 10,647
Therefore, there are 10,647 different ways to set up a committee of 4 people from a group of 10 people.