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##### What is the probability she gets exactly 3 that are the same color?

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A vase ccontains 16 yellow, 12 green, 9 purple and 3 red marbles. if lily randomly reaches in the vase and randomly pulls out 5 marbles without replacement, what is the probability she gets exactly she gets 3 that are the same color

Apr 22nd, 2015

THREE YELLOWS:
From the 16 yellows choose 3 --> 16C3 = 560
From the 24 non-yellows choose 2 --> 24C2 = 276
560 x 276 = 154,560 ways

THREE GREENS
From the 12 greens choose 3 --> 12C3 = 220
From the 28 non-greens choose 2 --> 28C2 = 378
220 x 378 = 83,160 ways

THREE PURPLES
From the 9 purples choose 3 --> 9C3 = 84
From the 31 non-purples choose 2 --> 31C2 = 465
84 x 465 = 39,060 ways

THREE REDS
From the 3 reds choose 3 --> 3C3 = 1
From the 37 non-reds choose 2 --> 37C2 = 666
1 x 666 = 666 ways

THREE OF ANY COLOR
154,560 + 83,160 + 39,060 + 666 = 277,446 ways

Now count the number of ways to get *any* 5 marbles.

ANY 5 MARBLES
From the 40 marbles choose 5 --> 658,008 ways

Finally compute the probability:
P(exactly 3 of the same color) = 277,446 / 658,008

That can be reduced to:
3557 / 8436
~42.16%

Apr 22nd, 2015

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Apr 22nd, 2015
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Apr 22nd, 2015
Sep 21st, 2017
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