Discrete Mathematics with Graph Theory (3rd Edition) 176

# Discrete Mathematics with Graph Theory (3rd Edition) 176 -...

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174 Solutions to Exercises First die 17. (a) Here are the possibilities. There are five ways to get a -S::;"e-c-o-n-=-d-:dc:-ie-t--::-t-=-+--:-+-:::-t-:::- total of eight. (b) Here are the possibilities. There are six ways to get a total of seven. (c) There are 5 + 6 = 11 ways to get an eight or a seven. First die Second die 6 1 (d) Getting doubles means two l's, two 2's, two 3's, two 4's, two 5's or two 6's. There are six ways to get doubles. 19. (a) 6 x 6 = 36; (b) 6 5 = 7776; (d) Since there are 6 n ways in which the dice can land and in precisely six of these ways the dice all land the same, the answer is 6 n - 6. 20. (a) [BB] HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT. There are 16 possibilities in all. (b) 4 ways; (b) 6 ways; (c) 4 ways; (d) 4 + 6 + 4 + 1 = 15 ways. 21. (a) 9 ·10·10·10·10 = 90,000; (b) 9·9·8·7·6 = 27,216; (c) 90000-27216 = 62,784. 22. (a) [BB] 26 x 26 x 26 x 10 x 9 x 8
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