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How many different ways can 3 cubes be painted if each cube
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25 Mar 2019, 11:36
25 Mar 2019, 11:36
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Question Stats:
18% (01:56) correct
81% (01:01) wrong based on 49 sessions
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How many different ways can 3 cubes be painted if each cube is painted one color and only the 3 colors red, blue, and green are available? (Order is not considered, for example, green, green, blue is considered the same as green, blue, green.)
(A) 2
(B) 3
(C) 9
(D) 10
(E) 27
(A) 2
(B) 3
(C) 9
(D) 10
(E) 27
Re: How many different ways can 3 cubes be painted if each cube
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29 Oct 2019, 03:38
29 Oct 2019, 03:38
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Consider 3 scenarios:
(1) all 3 the same colour... 3 options
(2) all 3 different colours... 1 option
(3) 2 of 1 colour and 1 of another colour (so we're using 2 of the 3 colours): 3C2 gives us the possible 2 colour choices. However, we need to double it, since if we choose R and B we could have RRB or RBB.
So, 3C2 * 2 = 3 * 2 = 6
3 + 1 + 6 = 10 possibilities.
(1) all 3 the same colour... 3 options
(2) all 3 different colours... 1 option
(3) 2 of 1 colour and 1 of another colour (so we're using 2 of the 3 colours): 3C2 gives us the possible 2 colour choices. However, we need to double it, since if we choose R and B we could have RRB or RBB.
So, 3C2 * 2 = 3 * 2 = 6
3 + 1 + 6 = 10 possibilities.
General Discussion
Re: How many different ways can 3 cubes be painted if each cube
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13 Aug 2026, 00:15
13 Aug 2026, 00:15
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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