How many solutions are there to the equation 10 = a + b + c with each of a, b, and c a whole number greater than or equal to zero?

Question

Mathematics

Nathanial Joseph

8 August, 18:58

How many solutions are there to the equation 10 = a + b + c with each of a, b, and c a whole number greater than or equal to zero?

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Derick Kramer · Answer 1

If a is fixed and b, c are unknowns then the equation b+c=10-a has 11-a solutions. They are pairs (b, c) : (0,10-a), (1,9-a), (2,8-a), ... (10-a, 0). As a runs from 0 to 10 we have total number of solutions (11-0) + (11-1) + ... (11-1) = 11+10 + ... + 1 = (1+11) * 11/2=66.