A bag contains 3 black, 4 white and 2 red balls, all the balls being different. The number of selections of at most 6 balls containing balls of all the colours, is

Options

A. `42xx4!`
B. `2^(6)xx4!`
C. `(2^(6)-1)4!`
D. none of these

Explanation

To solve the problem of selecting at most 6 balls from a bag containing 3 black, 4 white, and 2 red balls, ensuring that at least one ball of each color is included, we can follow these steps:

### Step 1: Identify the total number of balls
We have:
- 3 black balls
- 4 white balls
- 2 red balls

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