Nine balls one drawn simultaneously from a bad containing 5 white and 7 black balls. The probability of drawing 3 white and 6 black balls is

Step-by-step solution

Out of 12 balls we have to draw 9 balls. Therefore, selecting 9 balls from 12 balls can be done in n S = C 9 12   ways = 12 ! 9 ! × 3 ! = 220 Now, number of ways for selecting 3 white balls will be = C 3 5 = 5 ! 3 ! × 2 ! = 10 Number of ways for selecting 6 black balls will be = C 6 7 = 7 ! 6 ! × 1 ! = 7 Therefore, total number of ways for selecting 3 white and 6 black balls n P = 10 × 7 = 70 Therefore, probability of getting 3 white and 6 black balls = n P n S = 70 220 = 7 22