High School

A box contains 6 white and 5 black balls. Find the number of ways 4 balls can be drawn from the box if:

(i) Two must be white
(ii) All of them must have the same color

A) (i) 126, (ii) 126
B) (i) 126, (ii) 330
C) (i) 330, (ii) 126
D) (i) 330, (ii) 330

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.