Question

If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then, the probability that the drawn balls are of different colours is:

Options

• `1/66`

• `3/66`

• `19/66`

• `47/66`

Answer 1

`47/66`

Explanation:

Given, Number of white balls = 3

Number of Black balls = 4

Number of Red balls = 5

Total no. of balls (ways) = 12

Total no. of ways of drawing 2 balls out of 12 balls

= ¹²C₂

= `(12!)/(10!2!)`

= 66

Total no. of ways of drawing 2 balls of different colours

= 1 white 1 black + 1 black 1 red + 1 red 1 white

= ³C₁ × ⁴C₁ + ⁴C₁ × ⁵C₁ + ⁵C₁ × ³C₁

= 3 × 4 + 4 × 5 + 5 × 3

= 47

So, the probability of drawing 2 balls of different colours

= `47/66`