math414 hw1

math414 hw1 - n = 4 colors is P(4 3 = 4 Â 3 Â 2 = 24...

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SOLUTIONS FOR HWK # 1 1.1-2 (a) S= { bbb,gbb,bgb,bbg,bgg,gbg,ggb,ggg } . Note that n = 2 ,r = 3, and here we consider ordered samples with replacement so the size of the outcome space is n r = 8. (b) { female,male } . (c) { 000,001,002,. ..,999 } . Problem B . The size of the outcome space is 8. A = { bgg,gbg,ggb,ggg } ,P ( A ) = 4 8 = 1 / 2. B = { bgg,gbg,ggb } ; P ( B ) = 3 8 . C = { ggb,ggg } ; P ( C ) = 2 8 = 1 4 . D = B . E = B . 1.3-1 The number of ordered samples of size r = 4 with possible repetitions from n = 8 objects is 8 4 = 4096. 1.3-2 The number of ordered samples of r = 3 diﬀerent colors from
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Unformatted text preview: n = 4 colors is P (4 , 3) = 4 Â· 3 Â· 2 = 24. 1.3-3 (a) Step 1 . The r = 2 letters can be chosen with possible repetition from n = 26 letters 26 2 ways; Step 2 . The r = 4 digits can be chosen (with possible repetition) 10 4 ways. The number of diï¬€erent license plates is 26 2 Â· 10 4 = 6 , 760 , 000. (b) 26 3 Â· 10 3 = 17 , 576 , 000. 1.3-4 P (9 , 4) = 9! 5! = 3024. 1.3-5 (a) P (4) = 4! = 24. (b) 4 4 = 256. 1...
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