Exercise · ZW-INTEGER-COMPOSITION-007 · ★★☆ Intermediate
How many compositions of n=6 have exactly 3 parts?
Choose one option.
Show answer
- C. 10
Explanation
With k=3 we get \(\binom{5}{2}=10\), by choosing 2 separators among 5 gaps. The option of 20 is \(\binom{6}{3}\), which confuses n-1 with n.
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
- ZW-INTEGER-COMPOSITION-001 How many compositions of n=3 exist in total?
- ZW-INTEGER-COMPOSITION-002 How many compositions of n=4 have exactly 1 part?
- ZW-INTEGER-COMPOSITION-003 If n=5, how many gaps between units are there?
- ZW-INTEGER-COMPOSITION-004 What is the binomial coefficient binom42?
- ZW-INTEGER-COMPOSITION-005 How many compositions of n=2 exist?
- ZW-INTEGER-COMPOSITION-006 How many compositions of n=5 have exactly 2 parts?
- ZW-INTEGER-COMPOSITION-008 How many compositions of n=4 have at least 3 parts?
- ZW-INTEGER-COMPOSITION-009 How many compositions of n=6 have all parts odd?