Q: The number of solutions of x_{1} + x_{2} + x_{3} = 51 (x_{1} ,x_{2} , x_{3} being odd natural numbers) is

(A) 300

(B) 325

(C) 330

(D) 350

**Click to See Answer : **

Sol. Let odd natural numbers be 2a – 1 , 2b -1 , 2c – 1 ; where a, b, c are natural numbers

2a – 1 + 2b- 1 + 2c- 1 = 51

⇒ a + b + c = 27

a ≥ 1, b ≥ 1, c ≥ 1 …(1)

No. of solutions of (1) is coefficient of x^{24} in (1-x)^{-3}

= ^{26}C_{2} = 13 × 25 = 325

Hence (B) is the correct answer.