Question

A partition of a positive integer $n$ is any way of writing $n$ as a sum of one or more positive integers, in which we don't care about the order of the numbers in the sum. For example, the number 4 can be written as a sum of one or more positive integers (where we don't care about the order of the numbers in the sum) in exactly five ways: \[4,\; 3 1,\; 2 2,\; 2 1 1,\; 1 1 1 1.\] So 4 has five partitions. What is the number of partitions of the number 7

Answer 1

There are 15 partitions for the number 7. Where the partitions are nothing but writing an integer in different ways as a sum of two or more integers.

What is a partition?

A partition of a positive integer is the way of writing the integer as a sum of one or more positive integers. Where the order of the integers in the sum is not considered.

What is the number of partitions of the number 7?

There are 15 partitions. They are as follows:

1. 7
2. 1+6
3. 2+5
4. 3+4
5. 1+1+5
6. 1+2+4
7. 1+3+3
8. 2+2+3
9. 1+1+1+4
10. 1+1+2+3
11. 1+2+2+2
12. 1+1+1+1+3
13. 1+1+1+2+2
14. 1+1+1+1+1+2
15. 1+1+1+1+1+1+1

These are the 15 possible partitions of the number 7.

Learn more about the partition of an integer here:

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