2. A club has seven members. Three are to be chosen as a group to a national meeting. A) How many distinct groups of three can be chosen? B) If the club contains four men and three women, how many distinct groups of three contain two men and one woman? c) If the club contains four men and three women, how many distinct groups of three contain at least one woman?
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.
2. A club has seven members. Three are to be chosen as a group to a national meeting.
A) How many distinct groups of three can be chosen?
B) If the club contains four men and three women, how many distinct groups
of three contain two men and one woman?
c) If the club contains four men and three women, how many distinct groups
of three contain at least one woman?
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