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# 6 - a In how many ways can hats and gloves be returned so...

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1 d n = n ![1 1 1! + 1 2! · · · + ( 1) n 1 n ! ]

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2 Only the numbered squares are part of this chessboard C .
3

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4
5 Determine the rook polynomial for the chessboard from Fig. 8.8 using the recurrence relation (4).

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6 The number of ways we can seat these four relatives and satisfy (a) - (d) is the number of ways four nontaking rooks can be placed on the chessboard made up of noncrossed squares. If the number of crossed squares is smaller than the number of noncrossed (7 < 13), we can obtain solution using the crossed chessboard instead. This time we employ the inclusion/exclusion.
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8 Five gentleness meet in pub and they all leave their hats and gloves at the entrance. As they are leaving they decide to take their belongings at random.
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Unformatted text preview: a) In how many ways can hats and gloves be returned so that no gentleman gets either of his possession, i.e. will not get his hat and will not get his gloves. b) In how many ways can hats and gloves be returned so that no gentleman gets back both their possession, i.e. if he gets hat, then will not get gloves, and vice versa. 9 A pair of dice, one red and one green, is rolled six times. What is the probability that every value came up on both the red and green die under the assumption that the ordered pair (1,1), (1,5), (2,1), (2,5), (3,6), (4,2), (4,4), and (5,4) did not come up?...
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