Question

27. A box contains 7 red, 6 white and 4 blue balls. How many selections of three balls on of each colour?
(a) 178
(b) 158
(c) 198
(d) 168​

Answer 1

If a box contains 7 red, 6 white and 4 blue balls then ways of selections of three balls of each color is option (d): 168.

Step-by-step explanation:

There are 3 different colors of balls in the box which are

Red = 7  balls

White = 6  balls

Blue = 4  balls

Now we have to make a selection of 3 balls of each color i.e., all of the 3 balls should be of a different color.

No. of ways of selecting 1 red ball from 7 balls = ⁷C₁

No.of ways of selecting 1 white ball from 6 balls = ⁶C₁

No.of ways of selecting 1 blue ball from 4 balls = ⁴C₁

Thus,  

3 balls of each colour can be selected in,

= ⁷C₁ * ⁶C₁ * ⁴C₁

= $\frac{7!}{6!*1!}$ * $\frac{6!}{5!*1!}$ * $\frac{4!}{3!*1!}$ …… [since nCr = $\frac{n!}{(n-r)!*r!}$]

= 7 * 6 * 4

= 168 ways

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