Disc-midterm-ans

Disc-midterm-ans - 1. In how many ways can we arrange a...

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Unformatted text preview: 1. In how many ways can we arrange a standard deck of 52 cards so that all cards of a given suit appear contiguously (for example, the &rst thirteen cards are spades, the next thirteen are diamonds, then all the hearts, and then all the clubs) ? Each suit can be arranged in 13! ways. The four suits can be ordered in 4! ways. So the number of ways to do this is (13!) 4 4! = 36 085 481 721 713 375 974 666 734 560 870 400 000 000 . 2. Let A = f 1 ; 2 ; f 3 ; 4 gg . Which of the following are true and which are false ? (a) 1 2 A is true (b) f 1 g 2 A is false: the elements of A are 1 , 2 , and f 3 ; 4 g . (c) f 1 g & A is true: because 1 2 A . (d) 3 2 A is false: the elements of A are 1 , 2 , and f 3 ; 4 g . (e) f 3 g 2 A is false: the elements of A are 1 , 2 , and f 3 ; 4 g . (f) f 3 g & A is false: because 3 is not an element of A . 3. Let A and B be sets such that j A j = 20 , j A [ B j = 30 , and j A \ B j = 3 . What is j B j ?...
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Disc-midterm-ans - 1. In how many ways can we arrange a...

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