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What could be the number of 5-letter sequences that can be generated u
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06 Nov 2023, 00:18
06 Nov 2023, 00:18
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Question Stats:
33% (02:13) correct
66% (02:34) wrong based on 9 sessions
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What could be the number of 5-letter sequences that can be generated using 5 of the 6 letters that consist of 1 A, 2 Bs, and 3 Cs?
Indicate all possible numbers.
(A) 6
(B) 10
(C) 15
(D) 20
(E) 28
(F) 30
(G) 36
Indicate all possible numbers.
(A) 6
(B) 10
(C) 15
(D) 20
(E) 28
(F) 30
(G) 36
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Re: What could be the number of 5-letter sequences that can be generated u
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26 Nov 2023, 20:42
26 Nov 2023, 20:42
1
One might complicate things by thinking of this question as on of combination problems. It can be solved in a lot easier way as follows:
The list of alphabets = {A,B,B,C,C,C}
From this list, we are to choose 5 alphabets. If you look closely, you will know that there are three ways of doing this:
1. You could pick both B's and all C's, {B,B,C,C,C}
In this case, the arrangements possible are 5!/(2!x3!) = 10
2. You could pick the single A, one of the B's and all C's, {A,B,C,C,C}
In this case, the arrangements possible are 5!/(3!) = 20
3. Lastly, you could pick the single A, both B's and two of the three C's,{A,B,B,C,C}
In which case, the arrangments possible are 5!/(2!x2!) = 30
Hence, the correct answer choices are B, D, and F
The list of alphabets = {A,B,B,C,C,C}
From this list, we are to choose 5 alphabets. If you look closely, you will know that there are three ways of doing this:
1. You could pick both B's and all C's, {B,B,C,C,C}
In this case, the arrangements possible are 5!/(2!x3!) = 10
2. You could pick the single A, one of the B's and all C's, {A,B,C,C,C}
In this case, the arrangements possible are 5!/(3!) = 20
3. Lastly, you could pick the single A, both B's and two of the three C's,{A,B,B,C,C}
In which case, the arrangments possible are 5!/(2!x2!) = 30
Hence, the correct answer choices are B, D, and F
gmatclubot
Re: What could be the number of 5-letter sequences that can be generated u [#permalink]
26 Nov 2023, 20:42
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