Question

If there are 5 red balls, 5 blue, 5 green, 5 yellow coloured balls, when the balls are identical except for the colour. The no. of ways can 8 balls be selected.

• A. 100
• B. 125
• C. 105
• D. 120

Answer 1

Answer: (B)

125

Answer 2

No. of ways = Co-efficient of x⁸ in (1 + x + x² + ..... x⁵)⁴

= Coefficient of x⁸ in $\left( \frac{1 - x^{6}}{1 - x} \right)^{4}$

= Coefficient of x⁸ in (1 - x⁶)⁴ (1 - x)^-4

= (1 - 4x⁶ .....) $\left( 1 +^{4}C_{1}x +^{5}C_{2}x^{2} + ....... \right)$.

Coefficient $\mathrm { x } ^ { 8 } = { } ^ { 11 } \mathrm { C } _ { 8 } - 4 ^ { 5 } \mathrm { C } _ { 2 } = \frac { 11 \times 1,1 \times 0 } { \not \times 2 } - \frac { 4 \times 5 \times 4 } { 2 }$ = 165 – 40 = 125.