A bag contains 'x' red balls '2x' white balls and '3x&a

Question

A bag contains 'x' red balls '2x' white balls and '3x' black balls. 3 balls are drawn at random. The probability that all the balls drawn are of different colors is 0.3 .How many white balls are present in the bag?

Options:

A . 2

B . 4

C . 5

D . 7

Answer: Option A
:
A
P(All different)=

(^{x} C_{1}) \times (^{2 x} C_{1}) \times (^{3 x} C_{1}) / (^{6 x} C_{3})

P(E)=

(6 x^{3}) \times \frac{6}{6 x} \times [(6 x - 1) \times (6 x - 2)] = \frac{3}{10}

or,

\frac{3 x^{2}}{[(6 x - 1) \times (6 x - 2)]} = \frac{3}{10}

10 x^{2} = 18 x^{2} - 9 x + 1

or, (x-1)(8x-1)=0
x can not be a fraction hence x=1
Total number of white balls= 2x=2

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