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Answer :
Final answer:
To draw 4 balls from a box that contains 6 white and 5 black balls, there are 150 ways to draw 2 white balls and 20 ways to draw 4 balls of the same color.
Explanation:
To find the number of ways 4 balls can be drawn from the box:
(i) Two must be white:
There are 6 white balls in the box. We need to choose 2 of them. The number of ways to choose 2 out of 6 white balls is given by the formula C(6, 2) = 6! / (2!(6-2)!) = 15.
After selecting 2 white balls, we need to choose the remaining 2 balls from the black balls. There are 5 black balls in the box, and we need to choose 2 of them. The number of ways to choose 2 out of 5 black balls is given by the formula C(5, 2) = 5! / (2!(5-2)!) = 10.
So, the total number of ways to draw 4 balls with 2 white balls is 15 * 10 = 150.
(ii) All of them must have the same color:
There are 6 white balls and 5 black balls in the box. To draw 4 balls of the same color, we either need to draw 4 white balls or 4 black balls. The number of ways to draw 4 white balls is given by the formula C(6, 4) = 6! / (4!(6-4)!) = 15. The number of ways to draw 4 black balls is given by the formula C(5, 4) = 5! / (4!(5-4)!) = 5.
So, the total number of ways to draw 4 balls with all of them having the same color is 15 + 5 = 20.
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