Exercise · ZW-INTEGER-COMPOSITION-005 · ★☆☆ Basic
How many compositions of n=2 exist?
Choose one option.
Show answer
- A. 2
Explanation
They are 2 and 1+1, so there are 2^(2-1)=2 compositions. The option of 3 would count 1+1 as two distinct cases, and the option of 4 misapplies the formula.
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-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-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?