To find out how many possible committees of two people can be formed from a group of six people, we can use the combination formula. A combination is a selection of items from a larger pool where the order does not matter. In mathematical terms, this is written as:
Number of combinations (nCr) = n! / [r! * (n - r)!]
where:
- n is the total number of items,
- r is the number of items to choose,
- n! represents the factorial of n, which is the product of all positive integers up to n,
- r! is the factorial of r,
- (n - r)! is the factorial of (n - r).
For this problem:
- n = 6 (because there are 6 people to choose from)
- r = 2 (because we are forming committees of 2 people)
So we plug in these values into the formula:
Number of combinations (6C2) = 6! / [2! * (6 - 2)!]
Let's calculate this step-by-step:
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
2! = 2 * 1 = 2
(6 - 2)! = 4! = 4 * 3 * 2 * 1 = 24
Now place these into the combination formula:
Number of combinations (6C2) = 720 / (2 * 24)
Number of combinations (6C2) = 720 / 48
Number of combinations (6C2) = 15
So, there are 15 different possible committees of two people that can be formed from a group of six people.
