Find the number of triples of positive integers (a,b,c) that satisfy a + b + c = 6.
There are these ways to make 6:
We can then sort this list into 3 dfferent, 2 different, and no different.
Lets start easy.
3 same gets us only one way to permutate the numbers. 1
2 same gives us 2! ways to permutate the numbers(But we don't have any 2s) 0
and three different gives us 3! ways to permute 6
We have 7 ways to make 6 out of non zero positive whole numbers.