Solutions from a student (dragged) 7

# Solutions from a student (dragged) 7 - 52 cards we need to...

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Problem 12 (counting awards) Part (a): We have 30 students to choose from for the Frst award, and 30 students to choose from for the second award, etc. So the total number of di±eren toutcomesisg ivenby 30 5 =24300000 Part (b): We have 30 students to choose from for the Frst award, 29 students to choose from for the second award, etc. So the total number of di±eren toutcomesisg ivenby 30 · 29 · 28 · 27 · 26 = 17100720 Problem 13 (counting handshakes) With 20 people the number of pairs is given by ± 20 2 ²
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Unformatted text preview: 52 cards we need to select Fve to form a poker hand thus we have ± 52 5 ² = 2598960 , unique poker hands. Problem 15 (pairings in dancing) We must Frst choose Fve women from ten in ± 10 5 ² possible ways, and Fve men from 12 in ± 12 5 ² ways. Once these groups are chosen then we have 5! pairings of the men and women. Thus in total we will have ± 10 5 ² ± 12 5 ² 5! = 252 · 792 · 120 = 23950080 , possible pairings....
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