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A company wanted to assign color codes to its 24 offices. If either a
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08 Aug 2023, 03:32
08 Aug 2023, 03:32
Expert Reply
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Question Stats:
66% (02:01) correct
33% (01:49) wrong based on 6 sessions
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A company wanted to assign color codes to its 24 offices. If either a single color or a pair of two different colors is chosen to represent each office and if each office is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for coding? (Assume that the order of the colors in a pair does not matter.)
A. 3
B. 4
C. 5
D. 6
E. 7
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A. 3
B. 4
C. 5
D. 6
E. 7
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Re: A company wanted to assign color codes to its 24 offices. If either a
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02 Oct 2023, 04:51
02 Oct 2023, 04:51
Can someone please give the solution?
I think, it should be B, since 4! = 24
I think, it should be B, since 4! = 24
A company wanted to assign color codes to its 24 offices. If either a
[#permalink]
02 Oct 2023, 05:40
02 Oct 2023, 05:40
Expert Reply
We can label each office with two colors . for example, red blue or red green
Now, essentially , we do have 6 offices and three colors. n is the single color and \(C^n_2 \geq 24\)
\(\frac{n+n!}{2!(n-2)}!\)
or
\(\frac{n+n(n-1)}{2} \geq 24\)
Put in it the answer choices only E works
Now, essentially , we do have 6 offices and three colors. n is the single color and \(C^n_2 \geq 24\)
\(\frac{n+n!}{2!(n-2)}!\)
or
\(\frac{n+n(n-1)}{2} \geq 24\)
Put in it the answer choices only E works
