There are 5! such permutations.ī) Let q and e be next to each other as qe. After that has happened, there are 4 ways to fill the third, 3 to fill the fourth, and so on. Then there are 5 ways to fill the first spot. There are 6! permutations of the 6 letters of the word square.Ī) In how many of them is r the second letter? _ r _ _ _ _ī) In how many of them are q and e next to each other?Ī) Let r be the second letter. In how many different ways could you arrange them?Įxample 2. The number of permutations of n different things taken n at a timeĮxample 1. We mean, "4! is the number of permutations of all 4 of 4 different things.") (To say "taken 4 at a time" is a convention. Thus the number of permutations of 4 different things taken 4 at a time is 4!. Therefore the number of permutations of 4 different things is 3 ways remain to choose the second, 2 ways to choose the third, and 1 way to choose the last. Let us now consider the total number of permutations of all four letters. abĪb means that a was chosen first and b second ba means that b was chosen first and a second and so on.
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