Multiple choice

A bag contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the bag and kept aside. From the remaining balls another ball is drawn and kept aside the first. This process is repeated till all the balls are drawn. Then probability that the balls drawn are in sequence of 2 black, 4 white and 3 red is

  1. $\displaystyle \frac {1}{1260}$
  2. $\displaystyle \frac {1}{7560}$
  3. $\displaystyle \frac {1}{210}$

  4. none of these
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A Correct answer
Explanation

Total balls = 9. The probability of picking the sequence (2 black, 4 white, 3 red) is (2/9 * 1/8) * (4/7 * 3/6 * 2/5 * 1/4) * (3/3 * 2/2 * 1/1). This simplifies to (2/72) * (24/840) * 1 = (1/36) * (1/35) = 1/1260.

AI explanation

The total number of balls is the sum of black, white and red balls, giving 2 plus 4 plus 3 for a total of 9 balls. The probability of drawing a specific sequence of all 9 balls is calculated by multiplying the individual probabilities of each draw. The calculation is (2/9) multiplied by (1/8) multiplied by (4/7) multiplied by (3/6) multiplied by (2/5) multiplied by (1/4) multiplied by (3/3) multiplied by (2/2) multiplied by (1/1), which equals 1/1260.

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