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Unformatted text preview: Solution to HW 3 Ning SUN August 6, 2009 5.1: 6, 18(a), 22, 32; 5.2: 4, 10, 14, 16 (b, c, d) , 25, 32, 38 5.1#6 n ( n 1) 5.1#18 • (a) The letters can appear rst or last, 2 ways. The number of ways of choosing 3 letters, repetition allowed and order is important is 26 3 , similarly 3 number 10 3 , so the answer is 2 · 26 3 · 10 3 = 35 , 152 , 000 ways. 5.1#22 The rst digit has 3 choices, each of the following digits has only 2 choices (they cannot be the same as the previous digit), so we have 3 · 2 9 = 1536 ways. 5.1#32 There are three overlapping letters: R, E and N. 10 letters in RECURRENCE , and 8 letters in RELATION . #(total outcomes)= 10 · 8 = 80 . #(desired outcomes)=(RR+EE+NN)= 3 · 1 + 3 · 1 + 1 · 1 = 7 . So the requested probability is 7 80 = 0 . 0875 . 5.2#4 1. Seating 4 di erent girls and 4 di erent boys at a long table is equivalent to having the 8 kids stand in line, so there are 8! = 40 , 320 ....
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This note was uploaded on 08/30/2010 for the course AMS 301 taught by Professor Arkin during the Spring '08 term at SUNY Stony Brook.
 Spring '08
 ARKIN

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