Question

A dice is thrown. If it shows n, n different balls are drawn from a box containing 6 balls of different colors. How many elements are there in the sample space, if the outcomes considered are the number of different color combination possible?

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Answer 1

Let's say the number turned up is 1

Then we can select a ball and the color will be noted down. Let's say the colors are represented by $C_1,C_2....C_6.$ So the 6 possible outcomes are

$\left(C_1\right),\left(C_2\right),\left(C_3\right),\left(C_4\right),\left(C_5\right),\left(C_6\right).$

This is same as 6 $C_1$ possibilities.

'2'turns up

We can now take two balls and the possible combination of colors will look like

$(C_1,C_2),(C_1,C_3).......(C_1,C_6),$

$(C_2,C_3).............(C_2,C_6)$

If we write this all, we will have is possible outcomes with 2.

This is same as $6C_2$.

Similarly if '3' turns up it will be $6C_3$ and for 6 it will be $6C_6$.

$\Rightarrow$ Total outcomes = $6C_1+6C_2+6C_3....6C_6$

= 63