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October 19th, 2016, 06:38 AM   #1
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Unhappy Probability/Combinations confusion

Hi everyone,

I'm having some difficulty understanding when to use combinations and when to just multiply specific probabilities together for a given outcome...

So we have 10 marbles, 7 red, 3 blue.

How do I find the probability of getting four red marbles in a row?

I tried two methods and they both seem correct to me, but they give me different results and I'm not sure why.

Probability of desired event = Number of desired events/ number of total events


(7/10) * (6/9) * (5/8 ) * (4/7) = 840/5040 = .166

-or-

(number of ways to choose 4 red marbles) = 1

(number of total ways to chose 4 marbles out of 10) =
(10 choose 4) =
(10*9*8*7)/(4*3*2*1) = 5040/24 = 210

1/210 = .0049


I'm not sure which is correct, and why the two methods give me different answers. Please Help!

Last edited by skipjack; August 7th, 2017 at 09:49 PM.
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August 7th, 2017, 09:52 PM   #2
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The first is correct.
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