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Question

The number of different solutions of the equations x + y + z = 12, where each of x,y and z is a positive integer, is

This question was previously asked in
CDS I 2020 Elementary Mathematics Previous Year Paper (02-Feb-2020)
The correct answer is

55

Place two dividers in the 11 gaps between 12 units, so that each of the three labelled variables receives at least one unit. The number of positive ordered solutions is \(\binom{11}{2}=55\).

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