From 5 married couples, we want to select a group of 3 people. How many choices are there if the group must contain a married couple? How many choices are there if the group is not allowed to contain a married couple?
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.
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From 5 married couples, we want to select a group of 3 people.
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How many choices are there if the group must contain a married couple?
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How many choices are there if the group is not allowed to contain a married
couple?
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