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A child must choose from among 3 balloons, each of a different color.

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Carcass
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A child must choose from among 3 balloons, each of a different color. [#permalink] New post   Updated on: 29 Apr 2023, 23:53
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A child must choose from among 5 balloons, each of a different color.

Quantity A
Quantity B
The number of combinations of 2 different balloons he can choose
The number of combinations of 3 different balloons he can choose


A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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C

Originally posted by Carcass on 19 Jan 2023, 10:44.
Last edited by Carcass on 29 Apr 2023, 23:53, edited 1 time in total.
Fixed typo
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Carcass
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Re: A child must choose from among 3 balloons, each of a different color. [#permalink] New post   18 Feb 2023, 06:54
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Upon further inspection, you can see that choosing 2 balloons out of 5 is the same as choosing 3 balloons out of 5: when you choose 2 items out of 5, you are simultaneously choosing to exclude 3 items from your choice. You are effectively dividing the 5 balloons into a “Yes” pool and a “No” pool. The second scenario is the reverse of this: you are saying “Yes” to 3 balloons and “No” to 2 balloons. There are the same number of ways to say “Yes” to 2 balloons out of 5 as there are to say “No” to 2 balloons out of 5.
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april989
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Re: A child must choose from among 3 balloons, each of a different color. [#permalink] New post   29 Apr 2023, 22:32
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Carcass I think the question has a typo. In the question it says 3 balloons, but in the explanation you but that the child chooses from 5 different balloons.
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Re: A child must choose from among 3 balloons, each of a different color. [#permalink] New post   29 Apr 2023, 23:54
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april989 wrote:
Carcass I think the question has a typo. In the question it says 3 balloons, but in the explanation you but that the child chooses from 5 different balloons.



Thank you sir. Apologize for the typo. The book was not that clear.

Many thanks :please:
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LuisMartinez
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Re: A child must choose from among 3 balloons, each of a different color. [#permalink] New post   20 Aug 2024, 09:26
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This is a combinations problem, not a permutations (order does not matter). In combinations it follows a symmetric pattern, the way that you can arrange 0 ballons is the same as the way you can arrange all 5 (1 way). Th way you can arrange 1 ballon is the same as arrange 4. Hence the correct answer is C, that is a cool way to solve it conceptually, no calculations needed.
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Re: A child must choose from among 3 balloons, each of a different color. [#permalink]
20 Aug 2024, 09:26
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