Isye 2027

# 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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