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A bag has 4 blue, 3 yellow and 2 green balls. The balls of

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A bag has 4 blue, 3 yellow and 2 green balls. The balls of  [#permalink]

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New post Updated on: 25 Feb 2018, 06:19
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Question Stats:

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A bag has 4 blue, 3 yellow and 2 green balls. The balls of the same color are identical. In how many
ways can a child picks ball(s) out of the bag? He could even decide to pick ZERO balls.

A. 60
B. 1260
C. 24
D. 120
E. 9

Originally posted by voodoochild on 30 Sep 2012, 09:13.
Last edited by pushpitkc on 25 Feb 2018, 06:19, edited 1 time in total.
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Re: A bag has 4 blue, 3 yellow and 2 green balls. The balls of  [#permalink]

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New post 30 Sep 2012, 11:24
5
With the blue ball there are 5 scenarios-->
0 blue ball being selected
1 blue ball being selected
2 blue ball being selected
3 blue ball being selected
4 blue ball being selected

And for each of these cases there is only one possibilty as they are identical.

So there are 5 ways to select the blue ball
Same is the case with 3 yellow (for which we have 4 possibilties) and 2 green balls(we have 3 possibilties)


so in total 5*4*3 = 60 possibilties..
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Re: A bag has 4 blue, 3 yellow and 2 green balls. The balls of  [#permalink]

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New post 30 Sep 2012, 12:04
Ok. But why can't we do Green balls: (2C0=1)+(2C1=2)+(2C2=1)= 4 ways ? See this thread : a-jar-contains-6-magenta-balls-139813.html

The balls are also identical in the above question. I am confused between these two threads....
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Re: A bag has 4 blue, 3 yellow and 2 green balls. The balls of  [#permalink]

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New post 30 Sep 2012, 13:24
1
voodoochild wrote:
Ok. But why can't we do Green balls: (2C0=1)+(2C1=2)+(2C2=1)= 4 ways ? See this thread : a-jar-contains-6-magenta-balls-139813.html

The balls are also identical in the above question. I am confused between these two threads....


All the Green balls are identical. We don't care which one(s) was(were) chosen, only how many. We are interested in the final "statistics": how many Green balls were chosen? We have 3 possibilities: 0, 1, or 2.
2C1 = 2, it's true, but choosing either Green ball, will have the same statistical result: one Green ball was chosen, and we don't care about which one of the two Greens, because they are absolutely identical!
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Re: A bag has 4 blue, 3 yellow and 2 green balls. The balls of  [#permalink]

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New post 16 Apr 2014, 14:23
I tried this problem using anagram grid

9! / 4! 3 ! 2! = 1260

Does anyone know what i'm missing to get to 60 as an answer here?

Thanks!
Cheers
J :)
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Re: A bag has 4 blue, 3 yellow and 2 green balls. The balls of  [#permalink]

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New post 18 Apr 2014, 11:10
1
jlgdr wrote:
A bag has 4 blue, 3 yellow and 2 green balls. The balls of the same color are identical. In how many ways can a child picks ball(s) out of the bag? He could even decide to pick ZERO balls.

A. 60
B. 1260
C. 24
D. 120
E. 9

I tried this problem using anagram grid

9! / 4! 3 ! 2! = 1260

Does anyone know what i'm missing to get to 60 as an answer here?

Thanks!
Cheers
J :)


We are not asked to find the number of arrangements of 4 blue, 3 yellow and 2 green balls, which would be 9!/(4!3!2!).

We are asked to find the number of selections from 4 blue, 3 yellow and 2 green balls, when there can be any number of balls selected from 0 to 9.

A bag has 4 blue, 3 yellow and 2 green balls. The balls of the same color are identical. In how many ways can a child picks ball(s) out of the bag? He could even decide to pick ZERO balls.

A. 60
B. 1260
C. 24
D. 120
E. 9

In a selection there can be:
0, 1, 2, 3, or 4 blue balls, so 5 cases;
0, 1, 2, or 3 yellow balls, so 4 cases;
0, 1, or 2 green balls, so 3 cases.

Total 5*4*3=60 selections.

Answer: A.

Hope it's clear.
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Re: A bag has 4 blue, 3 yellow and 2 green balls. The balls of  [#permalink]

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New post 18 Apr 2014, 12:34
please go thru below link:

math-combinatorics-87345.html#p785179

You can solve in seconds: (4+1)*(3+1)*(2+1) = 5*4*3 = 60
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Re: A bag has 4 blue, 3 yellow and 2 green balls. The balls of  [#permalink]

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New post 18 Aug 2018, 19:32
voodoochild wrote:
A bag has 4 blue, 3 yellow and 2 green balls. The balls of the same color are identical. In how many
ways can a child picks ball(s) out of the bag? He could even decide to pick ZERO balls.

A. 60
B. 1260
C. 24
D. 120
E. 9


For the blue balls, he can choose 0, 1, 2, 3 or all 4 blue balls. So he has 5 choices for selecting the number of blue balls. Similarly, for the yellow balls, he can choose 0, 1, 2 or all 3 yellow balls. So he has 4 choices for selecting the number of yellow balls. Last but not least, for the green balls, he can choose 0, 1, or all 2 green balls. So he has 3 choices for selecting the number of green balls. Therefore, the total number of ways he can choose the balls is:

5 x 4 x 3 = 60

Answer: A
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Re: A bag has 4 blue, 3 yellow and 2 green balls. The balls of &nbs [#permalink] 18 Aug 2018, 19:32
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