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# A jar holds 4 red, 3 green and 6 white marbles. How many dif

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Manager
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A jar holds 4 red, 3 green and 6 white marbles. How many dif [#permalink]

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09 Sep 2012, 04:54
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A jar holds 4 red, 3 green and 6 white marbles. How many different ways can you pick 6 marbles so that you have at least one of each color"

sorry : The source did not have any answer choices.
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- Stne

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Joined: 22 Mar 2011
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Re: A jar holds 4 red, 3 green and 6 white marbles. How many dif [#permalink]

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09 Sep 2012, 10:38
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premnath wrote:
stne wrote:
A jar holds 4 red, 3 green and 6 white marbles. How many different ways can you pick 6 marbles so that you have at least one of each color"

sorry : The source did not have any answer choices.

If 1 red , 1 green and 1 white are chosen, the we need to choose 3 more marbles from out of 3 red, 2 green, and 6 white marbles.
So, Form 3+2+5=10 marbles we need to choose 3 marbles.
This can be done $$^{10}C$$$$^3$$Ways.
$$={10*9*8*7!}/{7!*3!}$$
=120

Far too many possibilities. The balls of the same color are assumed to be identical, what matters is just the number of balls of each color.
R - red, G - green, W - white
After we have chosen one of each type, we need 3 more balls to chose from 3R, 2G and 5W.
The question is about choosing the colors rather than specific balls.

We can again choose one of each color - 1R, 1G, 1W - 1 possibility
2 of one color and the third one of a different color - choose the color for two balls, then the color for the one ball - 3*2 = 6 possibilities
3 balls of the same color - only 2 possibilities - we don't have 3G balls left

Therefore, a total of 1+6+2=9 possibilities.
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Re: A jar holds 4 red, 3 green and 6 white marbles. How many dif [#permalink]

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09 Sep 2012, 06:08
stne wrote:
A jar holds 4 red, 3 green and 6 white marbles. How many different ways can you pick 6 marbles so that you have at least one of each color"

sorry : The source did not have any answer choices.

If 1 red , 1 green and 1 white are chosen, the we need to choose 3 more marbles from out of 3 red, 2 green, and 6 white marbles.
So, Form 3+2+5=10 marbles we need to choose 3 marbles.
This can be done $$^{10}C$$$$^3$$Ways.
$$={10*9*8*7!}/{7!*3!}$$
=120
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Re: A jar holds 4 red, 3 green and 6 white marbles. How many dif [#permalink]

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09 Sep 2012, 07:21
stne wrote:
A jar holds 4 red, 3 green and 6 white marbles. How many different ways can you pick 6 marbles so that you have at least one of each color"

sorry : The source did not have any answer choices.

$$(x+x^2+x^3+x^4)(x+x^2+x^3)(x+x^2+x^3.......+x^6)$$

find the coefficient of$$x^6$$ in this expansion.
Re: A jar holds 4 red, 3 green and 6 white marbles. How many dif   [#permalink] 09 Sep 2012, 07:21
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