A committee of 5 is chosen from 10 men and 6 women. Determine the number of ways of selecting the committee if: (i) there are no restrictions (ii) it must contain 3 men and 2 women (iii) it must contain at least 3 men (iv) it must contain at least one of each sex.
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 committee of 5 is chosen from 10 men and 6 women. Determine the number of ways of selecting
the committee if:
(i) there are no restrictions
(ii) it must contain 3 men and 2 women
(iii) it must contain at least 3 men
(iv) it must contain at least one of each sex.
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