Problem
COM-B2-M09-P011 Distinct Parts of 11
#11
★★★☆☆ Level 3 of 5
Find the number of partitions of \(11\) into distinct positive parts.
Use the product \(\prod_{i=1}^{11}(1+x^i)\).
Each part \(i\) can be taken either once or not at all, so the generating function is \(\prod_{i=1}^{11}(1+x^i)\). The partitions are \(11\), \(10+1\), \(9+2\), \(8+3\), \(8+2+1\), \(7+4\), \(7+3+1\), \(6+5\), \(6+4+1\), \(6+3+2\), \(5+4+2\), \(5+3+2+1\). There are \(12\) of them.
A small problem emphasizing the difference between partitions and compositions.