Exercise · ZW-COMBINATIONS-WITH-REPETITION-002 · ★☆☆ Basic
3 donuts are chosen from 5 available types, with repetition and without order. How many selections are there?
Choose one option.
Show answer
- D. 35
Explanation
There are \(\binom{5+3-1}{3}=\binom{7}{3}=35\). The 10 is \(\binom{5}{3}\), which does not allow repetition.
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-006 2 items are chosen from 4 types, ignoring order. How many more selections are there if repetition i…
- ZW-COMBINATIONS-WITH-REPETITION-007 How many distinct monomials of degree 3 are there in the variables x,y,z?
- ZW-COMBINATIONS-WITH-REPETITION-008 In how many ways can 10 identical marbles be distributed into 4 distinct boxes, allowing empty boxe…
- 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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