Question

Number of integral solution of a+b+c =0, a≥-5, b≥-5 and c≥-5 is

• A. 272
• B. 136
• C. 240
• D. 120

Answer 1

Answer: (B)

136

Answer 2

Let a = x – 5, b = y – 5, c = z – 5, therefore

x ≥0, y ≥ 0, z≥ 0

Now we have to find, number of non negative integral solutions of

(x – 5) + (y – 5) + (z –5) = 0

ie., x + y + z = 15

Required ways = Coefficient of x¹⁵ in (1 – x)^-3 = $17C_{2} = 136$.