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Disc-a6 - 4 ± 3 3 ± 2 ± 1 = 5 ± 4 2 = 10 2 At an art...

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1. List all the size-three multisets whose elements are selected from the set f a; b; c g . Then give the stars-and-bars representation for each of the mul- tisets you listed. Check that the number of multisets you listed is the same as the number you get when evaluating the symbol °° 3 3 ±± according to the formula given in the text . multiset stars and bars h a; a; a i ° ° °jj h a; a; b i ° ° j ° j h a; a; c i ° ° jj° h a; b; b i °j ° °j h a; b; c i °j ° j° h a; c; c i °jj ° ° h b; b; b i j ° ° ° j h b; b; c i j ° °j° h b; c; c i j ° j ° ° h c; c; c i jj ° °° ²²
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Unformatted text preview: 4 ± 3 3 ± 2 ± 1 = 5 ± 4 2 = 10 2. At an art academy, there are 43 students taking ceramics , 57 taking paint-ing , and 29 taking sculpture . There are 10 students in both ceramics and painting , 5 in both painting and sculpture , 5 in both ceramics and sculp-ture , and 2 taking all three courses . Use the inclusion-exclusion formula to calculate how many students are taking at least one course at the art academy . 43 + 57 + 29 ² 10 ² 5 ² 5 + 2 = 111...
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