HW #3 and 4

C therefore the probability that a license plate with

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Unformatted text preview: so with no repetitions whatsoever, there are 156, 000 × 720 = 11, 232, 000 license plates. (c) Therefore, the probability that a license plate with no repetitions is chosen at random from among 156000 all possible license plates including those with repetitions is given by 11232000 = 108 (= 0.639). 169 22. (a) (This is a problem about aligning 20 objects that belong to 4 categories, (6As,5Bs,3Cs,6Ds)). 20! 20×19×···×2×1 There are in total 6!5!3!6! = ((720)(120)(6)(120) = 6, 518, 191, 680. (you may leave the fraction as it is) (b) (This is a similar problem about aligning 12 objects that belong to 4 categories, 12! = 7, 484, 400. The corresponding probability is hence (2!)6 7, 484, 400 = 0.0034.(you may leave the fraction as it is) 612 23. S: Spanish; R: Russian; C: Chinese P(having same native language) = P(SS or RR or CC) = P(SS ) + P(RR) + P(CC ) ￿5￿ ￿4￿ ￿3￿ +2+ = 2 ￿12￿ 2 = 0.288. 2 1 12! 2!2!2!2!2!2! =...
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