Exercise · ZW-COMBINATIONS-WITH-REPETITION-006 · ★★☆ Intermediate
2 items are chosen from 4 types, ignoring order. How many more selections are there if repetition is allowed than if it is not?
Choose one option.
Show answer
- A. 4
Explanation
Without repetition there are \(\binom{4}{2}=6\); with repetition, \(\binom{5}{2}=10\). The difference is 4, the selections with a doubled type.
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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- ZW-COMBINATIONS-WITH-REPETITION-005 6 objects are chosen from 4 types, with repetition and without order. How many selections are there?
- ZW-COMBINATIONS-WITH-REPETITION-007 How many distinct monomials of degree 3 are there in the variables x,y,z?
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- ZW-COMBINATIONS-WITH-REPETITION-009 How many nonnegative integer solutions does x_1+x_2+x_3+x_4≤ 5 have?
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