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How 10-element multisets can be made from the symbols {a,b,c,d}? many O 720 O 286 O 120 O 24

How 10-element multisets can be made from the symbols {a,b,c,d}? many O 720 O 286 O 120 O 24

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Question:** How many 10-element multisets can be made from the symbols {a, b, c, d}? **Options:** - ○ 720 - ○ 286 - ○ 120 - ○ 24 **Explanation:** This problem asks for the number of 10-element multisets that can be generated from a set of four symbols: {a, b, c, d}. A multiset allows for repeated elements. The solution involves using the "stars and bars" theorem, which is a common combinatorial technique for these types of problems. For a multiset of size 10 created from 4 different elements, the formula for combinations with repetition is given by: \[ \binom{n+k-1}{k} = \binom{10+4-1}{4-1} = \binom{13}{3} = 286 \] Therefore, the correct answer is 286.
Transcribed Image Text:**Question:** How many 10-element multisets can be made from the symbols {a, b, c, d}? **Options:** - ○ 720 - ○ 286 - ○ 120 - ○ 24 **Explanation:** This problem asks for the number of 10-element multisets that can be generated from a set of four symbols: {a, b, c, d}. A multiset allows for repeated elements. The solution involves using the "stars and bars" theorem, which is a common combinatorial technique for these types of problems. For a multiset of size 10 created from 4 different elements, the formula for combinations with repetition is given by: \[ \binom{n+k-1}{k} = \binom{10+4-1}{4-1} = \binom{13}{3} = 286 \] Therefore, the correct answer is 286.
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