perplexus.info :: Probability : Non-conformist choice

Non-conformist choice (Posted on 2024-03-14)

There are total 21 balls in a bag.
Out of them 7 are blue,
5 are green
and 9 are black.
You pick 4 balls randomly from the bag.

What is the probability that not all balls are of the same colour?

See The Solution Submitted by Ady TZIDON

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solution | Comment 1 of 4

The probability that all four are blue is 7*6*5*4/(21*20*19*18).
... that all are green: 5*4*3*2/(21*20*19*18)
... black: 9*8*7*6/(21*20*19*18)

(7*6*5*4 + 5*4*3*2 + 9*8*7*6)/(21*20*19*18) = 166/5985 =~ 0.0277360066833751

That's the probability that all are the same color. The probability they are not is then

1 - 166/5985 = 5819/5985 =~ 0.972263993316625

Posted by Charlie on 2024-03-14 09:05:26

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