A group has 10 men and 7 women. If 6 people are selected for a committee so that the majority of the committee members are women, how many such committees are possible?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
A group has 10 men and 7 women. If 6 people are selected for a committee so that the majority of the committee members are women, how many such committees are possible?
Total number of people are
For the committee to be made with majority women, number of women's must be at least . Therefore we must consider scenarios that a committee comprises of women correspondingly with men.
Number of ways women can be the majority :
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