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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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 Fall '11
 DANIELCONUS
 Statistics, Probability

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