ve balls are drawn from a bag containing6 white and 4 black balls. What; is theprobability that 3 are white and 2 black ?

Sure, here is the step by step solution:

Step 1: Identify the total number of balls. We have 6 white balls and 4 black balls, so the total is 10 balls.

Step 2: We need to find the probability of drawing 3 white balls and 2 black balls.

Step 3: The number of ways to draw 3 white balls from 6 is given by the combination formula C(n, r) = n! / [(n-r)!r!], where n is the total number and r is the number chosen. So, C(6, 3) = 6! / [(6-3)!3!] = 20.

Step 4: Similarly, the number of ways to draw 2 black balls from 4 is C(4, 2) = 4! / [(4-2)!2!] = 6.

Step 5: The total number of ways to draw 5 balls from 10 is C(10, 5) = 10! / [(10-5)!5!] = 252.

Step 6: The probability of drawing 3 white balls and 2 black balls is therefore (C(6, 3) * C(4, 2)) / C(10, 5) = (20 * 6) / 252 = 0.4762 or 47.62% when expressed as a percentage.