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**Combinations**

A **Combination** determines the number of possible arrangements of elements where the order of the selection is not important. The number of possible combinations where there are elements and we take at a time is given by the formula:

**Example: **How many ways a math competition team of 5 students can be chosen from 8 students?

##### This is a combination problem in which we have 8 members and we take 5 at a time:

**Example: **A committee of 6 people is to be chosen from a group of 4 men and 5 women. How many committees are possible if: a) there are no restrictions. b) one particular individual has to be on the committee.

##### a) We have to select 6 people out of 9 people:

##### b) Since a particular person is already on the committee, we have 8 people left to choose from. We have to select 5 people out of 8 people:

**Example: **A committee of 6 people is to be chosen from a group of 4 men and 5 women. How many committees are possible if: a) there has to be 3 men and 3 women in the committee. b) there has to be at least 2 men in the committee.

##### a)

##### b) If there has to be at least 2 men, then we have the following possible arrangements:

##### Hence we have to evaluate: