Question

The number of ways of selecting 10 balls out of an unlimited number of white, red, blue and green balls is

• A. 270
• B. 84
• C. 286
• D. 86

Answer 1

Answer: (C)

286

Answer 2

Let x₁, x₂, x₃, x₄ be the number of white, red, blue, green balls respectively that are selected. Then x₁ + x₂+ x₃ + x₄ = 10. The required of ways

= coefficient of y¹⁰ in (1+ y+ y² + y³ + . . .)⁴ = coefficient of y¹⁰ in(1 – y)^–4

= coefficient of y¹⁰ in (1 + ⁴C₁ y + ⁵C₂y² + ⁶C₃y³ + . . .)

= $13C_{3} = \frac{13 \times 12 \times 11}{2 \times 3} = 286$