11ProbHw3sol - IEOR 3658 Probability Prof Mariana...

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IEOR 3658 Assignment #3 Solutions Probability October 10, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #3 Solutions 1. The number of ways to deal 13 out of total 52 cards is (52 P 13). For the case of first king being the 13th card, there are (48 P 12) ways to deal the first 12 cards, and (4 P 1) for the 13th, so there are (48 P 12) × (4 P 1) ways for the case. To conclude, the probabibility is (48 P 12) × 4! (52 P 13) . 2. We can reformulate the problem. There’re 6 sections, one for each color. We want to dis- tribute 100 jelly beans into those 6 sections. If 10 jelly beans are put into ”Red” section then we have 10 red jelly beans. Now, the problem is how many combinations are possible. With 1 divider we can make 2 sections. Therefore, we only need 5 dividers to create 6 sections. Now, assign one slot for each bean and each divider. Since we have 100 jelly beans and 5 dividers we need 105 slots. The problem of how to divide 100 jelly beans is the same as how to assign 5 dividers among 105 slots. Once we assign the dividers the rest of slots are filled
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