How many 4-person committees are possible from a group of 5 men and 4 women if: a) Either Jim or Mary (but not both) must be on the committee. b) The committee includes at most two men. At most two men (m=0,m=1,m=2) c) The committee includes at least two men and at least one woman. At least two men and at least one woman (m=3or m=2 and w=1or w=2)
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.
How many 4-person committees are possible from a group of 5 men and 4 women if:
a) Either Jim or Mary (but not both) must be on the committee.
b) The committee includes at most two men.
At most two men (m=0,m=1,m=2)
c) The committee includes at least two men and at least one woman.
At least two men and at least one woman (m=3or m=2 and w=1or w=2)
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