Q: The number of solutions of x1 + x2 + x3 = 51 (x1 ,x2 , x3 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 x24 in (1-x)-3
= 26C2 = 13 × 25 = 325
Hence (B) is the correct answer.