## Forming a Committee of Four

A committee of four can be formed in many different ways, depending on the composition and restrictions. If there are no restrictions on composition, then the number of possible combinations is virtually limitless.

### Calculating the Number of Combinations

The number of possible combinations for a committee of four can be calculated using the formula nCr, where n is the total number of people available to choose from and r is the number of people needed for the committee. In this case, n would be equal to the total number of people available and r would be equal to 4. Therefore, the total number of possible combinations would be equal to nCr or (n!)/(r!(n-r)!).

For example, if there are 10 people available to choose from, then the total number of possible combinations would be equal to 10C4 or (10!)/(4!(10-4)!), which equals 210. This means that there are 210 different ways that a committee of four can be formed with no restrictions on composition.