hw1_418_10

# hw1_418_10 - 1. a) Since it is not restricted on the...

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1. a) Since it is not restricted on the repeat, there are altogether 26 choices for the ﬁrst two plates, and 10 choices for the next ﬁve plates. Then altogether 26 2 × 10 5 . b) This time two plates cannot the same. So, the ﬁrst plates has 26 choices, and the second plates will only have 25 choices. Similar for all the remaining ones. Then altogether 26 × 25 × 10 × 9 × 8 × 7 × 6. 4. a) Since each boy can play any of the instruments, and each of them will take one in- strument, the ﬁrst boy will have 4 choices, and the second one will have 3 choices. Then altogether 4! = 24. b) Since Jay and Jack can only play piano and drums, these two boys are restricted only on these 2 choices. As a result, the other two boys only restricted to the remaining two instruments. So altogether 2! × 2! = 4. 10. a) Since there is no any restrictions, the ﬁrst person will have 8 choices, and the next one will have 7 choices. Finally, we altogether have 8! arrangements. b)Since person A and B must sit together, we treat these two person as a whole unit, then similar to a) part, there are altogether 7! choices. Moreover, the order of A and B matters, so, the ﬁnal result is 2! × 7! = 10080 . c) Since no two woman and two man can be sit next to each other, we treat one woman

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## This note was uploaded on 01/23/2011 for the course STAT 418 taught by Professor G.jogeshbabu during the Fall '08 term at Penn State.

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hw1_418_10 - 1. a) Since it is not restricted on the...

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