14 chapter 1 foundations solution there are three

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Unformatted text preview: ). Here the possibilities for the second letter are slightly limited by the first letter, because the second letter must be different from the first. Thus, the choices of letter for each position are not independent. If the letter A is used in the first position, for example, it can’t be used in the second position. The problem is still quite simple, however, because the choice of letter for the first position does not affect the number of choices for the second position. And the first two choices don’t affect the number of choices for the third position. In general, the number of ways to order n distinct objects is n! = n · (n − 1) · · · 2 · 1. An ordering of n distinct objects is called a permutation, so the number of permutations of n distinct objects is n!. The next example indicates how to deal with cases in which the objects are not distinct. Example 1.3.3 How many orderings of the letters AAB are there, if we don’t distinguish between the two A’s? 14 CHAPTER 1. FOUND...
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