21127 Study Guide - Quiz Guide: Beek, Burh, Anagram
16 Dec 2015
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Recall the following formula for the number of ways to select k objects, unordered and with repetitions allowed, from n types of objects, and its corresponding proof: To choose k objects from n types of objects, there are(cid:0)k+n 1 (cid:1) ways. k. Proof: construct a sequence of length k + n 1 with k tokens and n 1 dividers. Selections with repetition (1) a clothing store makes 5 di erent colors of shirts (red, green, blue, white, and black): we need to buy 10 shirts. This is selection with repetition, where we select k = 10 objects from n = 5 types. Equivalently, it"s the number of solutions to x1+x2+x3+x4+x5 = 10 satisfying i [5]. xi n {0}. (cid:19) By the above formula, there are(cid:18)10 + 5 1. 14 13 12 11 (cid:18)14 (cid:19) 10: we need to acquire some shirts, either 10 or 11 or 12, we"re not sure yet.
