Exercise · ZW-COMBINATIONS-WITH-REPETITION-001 · ★☆☆ Basic
An ice cream shop has 3 flavors. In how many ways can 5 scoops be ordered, repeating flavors if desired and ignoring order?
Choose one option.
Show answer
- B. 21
Explanation
It is a combination with repetition: \(\binom{3+5-1}{5}=\binom{7}{5}=21\). Using \(3^5=243\) counts with order, and \(\binom{8}{5}=56\) adds one unit too many.
Review the concept: Combinations with repetition
A combination with repetition of size \(k\) from \(n\) types of object is an unordered selection of \(k\) objects in which each type may be chosen several times.
\[\binom{n+k-1}{k}\]
More practice problems: combinations with repetition
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