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A class is divided into four groups of four students each.

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A class is divided into four groups of four students each. [#permalink]

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New post 02 Feb 2012, 12:07
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A class is divided into four groups of four students each. If a project is to be assigned to a team of three students, none of which can be from the same group, what is the greatest number of distinct teams to which the project could be assigned?

(A) 4^3
(B) 4^4
(C) 4^5
(D) 6(4^4)
(E) 4(3^6)

My solution:

4C3 * 4 = 4^4 .
Is the formula used rightly selected although the answer agrees to OA?
[Reveal] Spoiler: OA
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Re: Selecting a team from four groups [#permalink]

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New post 02 Feb 2012, 12:22
Expert's post
docabuzar wrote:
Q. A class is divided into four groups of four students each. If a project is to be assigned to a team of three students, none of which can be from the same group, what is the greatest number of distinct teams to which the project could be assigned?

(A) 4^3
(B) 4^4
(C) 4^5
(D) 6(4^4)
(E) 4(3^6)

My solution:

4C3 * 4 = 4^4 .
Is the formula used rightly selected although the answer agrees to OA?


Basically we are asked to determine the # of different teams of 3 that can be formed so that no 2 members are from the same group.

\(C^3_4=4\) - choosing which 3 groups out of 4 will provide with a member;
\(C^1_4*C^1_4*C^1_4=4^3\) - choosing each member from the selected 3 groups ;

So, total # of different groups will be: \(4*4^3=4^4\).

Answer: B.

P.S. Answer is correct, formula and math is not: \(C^3_4*4=4^2\).
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Joined: 17 Jan 2012
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GMAT 1: 610 Q43 V31
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Re: A class is divided into four groups of four students each. [#permalink]

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New post 02 Feb 2012, 12:34
Thanks.

Its clear now. I m making the silly mistake of reading my 4*4 as 4^4 from the OA.
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Re: A class is divided into four groups of four students each. [#permalink]

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New post 06 Apr 2016, 23:23
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Re: A class is divided into four groups of four students each.   [#permalink] 06 Apr 2016, 23:23
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