Solutions from a student (dragged) 31

# Solutions from a student (dragged) 31 - Problem 5(dividing...

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Problem 5 (dividing gifts) We have 7 3 ways to select three gifts for the first child, then 4 2 ways to select two gifts for the second, and finally 2 2 for the third child. Giving a total of 7 3 · 4 2 · 2 2 = 210 , arrangements. Problem 6 (license plates) We can pick the location of the three letters in 7 3 ways. Once these positions are selected we have 26 3 di ff erent combinations of letters that can be placed in the three spots. From the four remaining slots we can place 10 4 di ff erent digits giving in total 7 3 · 26 3 · 10 4 , possible seven place license plates. Problem 7 (a simple combinatorial argument) Remember that the expression n r counts the number of ways we can select r items from n . Notice that once we have specified a particular selection of
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