In How many ways can one write a natural number M as a sum of N whole numbers?(adsbygoogle = window.adsbygoogle || []).push({});

Consider the two conditions;

1)the numbers appearing in the sum are distinct.

2)the numbers appearing in the sum are not necessary distinct.

eg1:eight can be written as a sum of 6 whole numbers as shown below

8=8+0+0+0+0+0

8=1+1+1+1+4+0

etc..(subject to condition 2)

eg2:8 can be written as a sum of 4 whole numbers as shown below

8=0+1+3+4

etc..(subject to condition 1)

Let me make the following notations

[tex]\Gamma[/tex](M,N) as the no of ways to partition M into N whole numbers subject to condition 1)

[tex]\Pi[/tex](M,N) as the no of ways to partition M into N whole numbers subject to condition 2)

this is no homework problem i formulated this on my own.

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# Partioning natural numbers

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