Question

One solution to the equation is a + b + c = 10 is

a=2 b=5 c=3
How many different whole-number solutions are there to
the equation ? Explain or show your reasoning.

Answer 1

Explanation:

Imagine placing 10 apples in a row.

We have an extra 2 baricades that we can place between any 2 apples, so that a total of 3 groups will be formed.

This is the same as choosing 2 of the 12 items to be barricades.

Hence the answer is 12C2 = 66.