Solutions from a student (dragged) 8

Solutions from a student (dragged) 8 - 4 = 94 total...

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Problem 16 (forced selling of books) Part (a): We have to select a subject from three choices. If we choose math we have ± 6 2 ² =15cho iceso fbookstose l l . I fwechoosesc iencewehave ± 7 2 ² =21cho iceso f books to sell. If we choose economics we have ± 4 2 ² =6choicesofbookstose l l . S inceeach choice is mutually exclusive in total we have 15 + 21 + 6 = 42, possible choices. Part (b): We must pick two subjects from ± 3 2 ² =3choices . Ifwedenotetheletter“M” for the choice math the letter “S” for the choice science, and the letter “E” for the choice economics then the three choices are (
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Unformatted text preview: · 4 = 94 total choices. Problem 17 (distributing gifts) We can choose seven children to give gifts to in ± 10 7 ² ways. Once we have chosen the seven children, the gifts can be distributed in 7! ways. This gives a total of ± 10 7 ² · 7! = 604800 , possible gift distributions. Problem 18 (selecting political parties) We can choose two Republicans from the ±ve total in ± 5 2 ² ways, we can choose two Democrats from the six in ± 6 2 ² ways, and ±nally we can choose three Independents from the four in ± 4 3 ² ways. In total, we will have ± 5 2 ² · ± 6 2 ² · ± 4 3 ² = 600 , di²erent committees....
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