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MATH 310, FALL 2003 (Combinatorial Problem Solving) Lecture 19, Friday, October 17

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5.3. Arrangements and Selections with Repetitions Homework (MATH 310#6F2): Read 5.4 Do 5.3: All odd numbered exercises. Turn in 5.3: 12,20,22,30 Volunteers: ____________ Problem: 12.

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Theorem 1 If there are n objects, with r 1 of type 1, r 2 of type 2,..., and r m of type m, where r 1 + r 2 +... + r m = n, then the number of arrangements of these n objects is P(n;r 1,r 2,..., r m ) where P(n;r 1,r 2,..., r m ) = n!/(r 1 !r 2 !...r m !)

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Theorem 2 The number of selections with repetitions of r objects chosen from n types of objects is C(r+n-1,r).

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