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