How many license plates can be made using either two or three letters followed by either two or three digits and contain no letter or digit twice?
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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a) How many license plates can be made using either two or three letters followed by either two or three digits and contain no letter or digit twice?
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b) The sixth permutation of the lexicographic permutations of the 24 elements of the set {I, 2, 3, 4} is 1432. Find the next ten permutations in lexicographic order after 1432.
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c) Suppose that a department contains 10 men and 15 women. How many ways are there to select a committee with six members if it must have
i. At most three women?
II. At least 1 woman and at least 1 man?
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