Twelve people are on a committee, seven women and five men. If a four-person subcommittee is to be chosen, how many such subcommittees can be formed with exactly two men and two women? A. 31 B. 210 c. 4 D. 240
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.
Twelve people are on a committee, seven women and five men. If a four-person subcommittee is to be chosen, how many such subcommittees can be formed with exactly two men and two women?
A. 31
B. 210
c. 4
D. 240
Since we are going to form a committee so here order does not matter. So we will use combination.
We can pick 2 men from 5 men in 5C2 ways.
We can pick 2 women from 7 women in 7C2 ways.
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