# Thread: A probability question

1. ## A probability question

A pool (infinite) of coloured marbles 7 colours in total with equal proportion. 4 marbles are chosen, what is the probability that at least 2 of the same colour.

I did 1-P(all different) which is 1-7/7*6/7*5/7*4/7

Also tried the "direct" approach

2 same: 1/7*1/7*6/7*5/7*4C2*7 where the 4C2 is to choose which 2 to be the same and 7 is to account for 7 colours

3 same: 1/7*1/7*1/7*6/7*4C3*7

4 same: 1/7*1/7*1/7*1/7*7

But when I add up it does not tally with my first approach.

What went wrong? Appreciate if anyone can help.

Thanks.

2. ## Re: A probability question

Originally Posted by acc100jt
A pool (infinite) of coloured marbles 7 colours in total with equal proportion. 4 marbles are chosen, what is the probability that at least 2 of the same colour.
I did 1-P(all different) .
You have absolutely the correct approach. But this is a multi-selection question.
The number of ways to select $N$ items from $K$ different possibilities is $\binom{N+K-1}{N}$
So $\binom{4+7-1}{4}=210$ See Here.

How many of those are all of the same colours?