elemprob-fall2010-page14

elemprob-fall2010-page14 - of the 24 total in 24 20 ways....

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many nonnegative integer solutions are there to the equation x 1 + x 2 + x 3 + x 4 + x 5 = 20. View this as putting 20 balls in 5 boxes, with x 1 in the first box, x 2 in the second, and so on. So there are 20 o ’s, a | for the first and last spot in a sequence, and 4 other | ’s. We can choose 20 spaces for the o ’s out
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Unformatted text preview: of the 24 total in 24 20 ways. An example. Consider the same question as the example above, but where each x i is at least 1. Answer: First put one ball in each box. This leaves 15 balls to put in 5 boxes, and as above this can be done 19 15 ways. 14...
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