Exercise · ZW-INTEGER-COMPOSITION-006 · ★★☆ Intermediate
How many compositions of n=5 have exactly 2 parts?
Choose one option.
Show answer
- D. 4
Explanation
With k=2 we get \(\binom{4}{1}=4\): 1+4, 2+3, 3+2 and 4+1. The option of 10 corresponds to \(\binom{5}{2}\), which uses n instead of n-1.
Review the concept: Integer composition
A composition of a positive integer n is a way of writing it as an ordered sum of positive integers, where the order of the summands matters.
\[\binom{n-1}{k-1}\]
More practice problems: integer composition
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