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Unformatted text preview: r = n, x i > m i y i i = 1 r = n i = 1 r m r k 8 3 4 3 + 2 1 4 2 = 896 possible committees n 1 rk 1 = n 1 n r + k P21 : Each path is a string of 7 characters, 4Rs(Right) and 3 Us(Up). The number of paths corresponds to the number of ways of selecting the character positions for either the 4Rs (or equivalently the 3Us). e.g., RRUURUR. P22 : There are Therefore there are P32: (a) Number of nonnegative solutions to is (b) Professor Heffes 7 4 = 35 4 2 paths from A to the circle and 3 2 paths from the circle to B. 4 2 3 2 = 18 paths from A to B passing through the circlethe circle x i i = 1 6 = 8 13 5 # nonnegative solutions to x i i = 1 6 = 5 # nonnegative solutions to y i i = 1 6 = 3 = 10 5 8 5...
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 Spring '08
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