A bag contains 6 black, 7 white, and 8 green balls. In how many ways can we select groups of balls where each group consists of (a) 4 black or 4 white balls; (b)4 black and 4 white balls;,(c) 4 balls all of the same color; (d) 4 balls of each color?

ANS:

Solution:

a) 4 black or 4 white balls:

We can choose 4 black balls out of 6 in 6C4 ways and choose 4 white balls out of 7 in 7C4 ways. So, the total number of ways to select 4 black or 4 white balls is:

6C4 + 7C4 = 15 + 35 = 50

b) 4 black and 4 white balls:

There are two ways to choose 4 black balls from 6 and 4 white balls from 7:

  • Black 4, White 4: 6C4 * 7C4 = 15 * 35 = 525 ways.
  • White 4, Black 4: 7C4 * 6C4 = 35 * 15 = 525 ways.

Adding both ways, we get 525 + 525 = 1050 ways.

c) 4 balls of the same color:

We can choose 4 balls out of 6 black balls in 6C4 ways, 4 out of 7 white balls in 7C4 ways, and 4 out of 8 green balls in 8C4 ways. The total number of ways to select 4 balls of the same color is:

6C4 + 7C4 + 8C4 = 15 + 35 + 70 = 120

d) 4 balls of each color:

We can choose 4 black balls out of 6 in 6C4 ways, 4 white balls out of 7 in 7C4 ways, and 4 green balls out of 8 in 8C4 ways. So, the total number of ways to select 4 balls of each color is:

6C4 * 7C4 * 8C4 = 15 * 35 * 70 = 34300

Leave a Comment