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?
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 C1,C2....C6. So the 6 possible outcomes are
(C1),(C2),(C3),(C4),(C5),(C6).
This is same as 6 C1 possibilities.
'2'turns up
We can now take two balls and the possible combination of colors will look like
(C1,C2),(C1,C3).......(C1,C6),
(C2,C3).............(C2,C6)
If we write this all, we will have is possible outcomes with 2.
This is same as 6C2.
Similarly if '3' turns up it will be 6C3 and for 6 it will be 6C6.
⇒ Total outcomes = 6C1+6C2+6C3....6C6
= 63