Question

If a, b, c, d are odd natural numbers such that

a + b + c + d = 20 then the number of values of a, b, c, d is-

• A. 165
• B. 455
• C. 310
• D. 255

Answer 1

Answer: (A)

165

Answer 2

Let a = 2p + 1, b = 2q + 1, c = 2r + 1, d = 2s + 1

where p, q, r and s are non-negative integers.

\ 2p + 1 + 2q + 1 + 2r + 1 + 2s + 1 = 20 or p + q + r + s = 8

The required number of solutions = The number of non- negative integral solutions of (p + q + r + s= 8),

$\frac{(8 + 3)(8 + 2)(8 + 1)}{6}$ = 165 (Now solve it)