If a, b, c are odd positive integers, then number of integral solutions of a + b + c = 13, is

(a) 14 , (b) 21 , (c) 28 , (d) 56

The correct answer is option b) 21

explaination ::

Let a = 2k + 1, b = 2l + 1, c = 2m + 1

where k, l, m are whole number

a + b + c = 13

2k + 1 + 2l + 1 + 2z + 1 = 13

or, x + y + z = 5

The number of integrals solutions

\(=^{5+3-1}C_{3-1}=^7C_2\)

\(={7.6\over 1.2}=21\)

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