5.5_problems

# 5.5_problems - EECS 203 Supplemental Study Material for...

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EECS 203 Supplemental Study Material for Section 5.5 5.5.12 . How many different combinations of pennies, nickels, dimes, quarters, and half dollars can a piggy bank contain if it has 20 coins in it? Solution : There are 5 things to choose from, repetitions allowed, and we want to choose 20 things, order not important. Therefore by Theorem 2 the answer is 5.5.30 . How many different strings can be made from the letters in MISSISSIPPI , using all the letters? Solution : By Theorem 3 the answer is . 5.5.38 . A professor packs her collection of 40 issues of a mathematics journal in four boxes with 10 issues per box. How many ways can she distribute the journals if (a) each box is numbered, so that they are distinguishable? (b) the boxes are identical, so that they cannot be distinguished? Solution : (a) Theorem 4 says that the answer is . (b) Each distribution into identical boxes gives rise to distributions into labeled boxes, since once we have made the distribution into unlabeled boxes we can arbitrarily label the boxes. Therefore the answer is the same as the answer in part (a) divided by 24, namely
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