# HW2 - not true(b Show that the number of subsets of an...

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CSE21 FA11 Homework #2 (10/3/11) In this homework, we will consider “ordinary” decks of playing cards which have 52 cards, with 13 of each of the four suits (Hearts, Spades, Diamonds and Clubs) with each suit have the 13 ranks (Ace, 2, 3, . . . , Jack, Queen, King). (See the text if you need more details). 2.1. (a) How many diﬀerent rearrangements of all the letters in UNSCRUPULOUS are there? (b) How many diﬀerent rearrangements of all the letters in supercalifragilisticexpialidocious are there? 2.2. A 20-member club must have a president, vice-president, secretary, and a treasurer, as well as a three-person nominating committee. If the oﬃcers mud be diﬀerent people, and if no oﬃcer may be on the nominating committee, in how many ways could the oﬃcers and nominating committee be chosen? Answer the same question if oﬃcers may be on the nominating committee. 2.3. (a) Explain why n i =0 ( - 1) k ( n k ) = 0. At least, this is what Problem 17 on p. 32 of our text claims. When is this statement

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Unformatted text preview: not true? (b) Show that the number of subsets of an n-set having an even number of elements is equal the the number of subsets of an n-set having on odd number of elements (when n > 0). 2.4 (a) How many 5-card hands are there where all the cards have the same suit? (b) How many 5-card hands are there where all the cards belong to at most two suits? (c) How many 5-card hands are there where all the cards have at most two diﬀerent ranks? 1 2.5 (a) How many 5-card hands (from an ordinary deck) have at least one card of each suit? (b) How many 6-card hands have at least one card of each suit? 2.6 (a) In how many ways can 15 (identical) jellybeans be distributed to 4 boys and 4 girls if each girl must get at least one jellybean? (b) In how many ways can 15 (identical) jellybeans be distributed to 4 boys and 4 girls if each girl must get at least one jellybean and no boy can get more than one jellybean? 2...
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HW2 - not true(b Show that the number of subsets of an...

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