Exercise · ZW-INTEGER-COMPOSITION-008 · ★★☆ Intermediate
How many compositions of n=4 have at least 3 parts?
Choose one option.
Show answer
- B. 4
Explanation
With 3 parts there are \(\binom{3}{2}=3\) cases and with 4 parts there is 1, total 4. The option of 5 also includes the compositions with 2 parts, which do not count.
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-007 How many compositions of n=6 have exactly 3 parts?
- ZW-INTEGER-COMPOSITION-009 How many compositions of n=6 have all parts odd?