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Eight students were to be seated along two rows such that four student

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Bunuel
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Eight students were to be seated along two rows such that four student [#permalink] Eight students were to be seated along two rows such that four student   10 Jun 2021, 06:15
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60% (02:24) correct 40% (03:00) wrong based on 98 sessions
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Eight students were to be seated along two rows such that four students will be seated in each of the two rows called A and B. Two of the eight students definitely want to be seated in row A while one of them definitely wants to be seated in row B. In how many different ways can the eight students be seated?

(A) 5,760
(B) 5,960
(C) 6,500
(D) 6,760
(E) 7,160
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Eight students were to be seated along two rows such that four student [#permalink] Eight students were to be seated along two rows such that four student   10 Jun 2021, 06:26
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Bunuel wrote:
Eight students were to be seated along two rows such that four students will be seated in each of the two rows called A and B. Two of the eight students definitely want to be seated in row A while one of them definitely wants to be seated in row B. In how many different ways can the eight students be seated?

(A) 5,760
(B) 5,960
(C) 6,500
(D) 6,760
(E) 7,160

Let students are
PQRSTUVW

Let, P and Q want to be in Row A
R wants to be in Row B

i.e. we need only two more students for Row A (other than P & Q) and those two should be selected from remaining 5 students (P Q and R have fixed rows already)

i.e. ways to select those two students for row A = \(^5C_2 = 10\)

Now arrangements of first row can be done in 4! ways
Now arrangements of Second row can be done in 4! ways

Total Outcomes = \(^5C_2*4!*4!= 10*24*24 = 5760\)

Answer: Option A
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Niveditha28
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Re: Eight students were to be seated along two rows such that four student [#permalink] Eight students were to be seated along two rows such that four student   10 Jun 2021, 07:33
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IMO option A
My Approach

row 1 - - - -. 2 students are seated in row 1 SO --> s1 s2 - - . Any two seats can be selected out of 4 seats so 4C2 ways
row 2 - - - - 1 student is seated in row 2 .SO --> s3 - - -Any one seat can be selected out of 4 seats so 4C1 ways

5 spaces to arrange the remaining 5 students out of 8 i,e 5!.
Now they have choice to choose any one of two rows. hence 2C1

Hence 5! x 2C1 x 4C2 x 4C1 = 240*4*6= 5760 ways
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Re: Eight students were to be seated along two rows such that four student [#permalink] Eight students were to be seated along two rows such that four student   28 Jul 2024, 05:54
GMATinsight wrote:
Bunuel wrote:
Eight students were to be seated along two rows such that four students will be seated in each of the two rows called A and B. Two of the eight students definitely want to be seated in row A while one of them definitely wants to be seated in row B. In how many different ways can the eight students be seated?

(A) 5,760
(B) 5,960
(C) 6,500
(D) 6,760
(E) 7,160

Let students are
PQRSTUVW

Let, P and Q want to be in Row A
R wants to be in Row B

i.e. we need only two more students for Row A (other than P & Q) and those two should be selected from remaining 5 students (P Q and R have fixed rows already)

i.e. ways to select those two students for row A = \(^5C_2 = 10\)

Now arrangements of first row can be done in 4! ways
Now arrangements of Second row can be done in 4! ways

Total Outcomes = \(^5C_2*4!*4!= 10*24*24 = 5760\)

Answer: Option A


­Why are you not selecting students for row B? (why do you assume the remaining ones is ok) - something like 5C3 for row B

Could you help Bunuel ?­
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Bunuel
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Re: Eight students were to be seated along two rows such that four student [#permalink] Eight students were to be seated along two rows such that four student   29 Jul 2024, 00:11
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miquelperezn wrote:
GMATinsight wrote:
Bunuel wrote:
Eight students were to be seated along two rows such that four students will be seated in each of the two rows called A and B. Two of the eight students definitely want to be seated in row A while one of them definitely wants to be seated in row B. In how many different ways can the eight students be seated?

(A) 5,760
(B) 5,960
(C) 6,500
(D) 6,760
(E) 7,160

Let students are
PQRSTUVW

Let, P and Q want to be in Row A
R wants to be in Row B

i.e. we need only two more students for Row A (other than P & Q) and those two should be selected from remaining 5 students (P Q and R have fixed rows already)

i.e. ways to select those two students for row A = \(^5C_2 = 10\)

Now arrangements of first row can be done in 4! ways
Now arrangements of Second row can be done in 4! ways

Total Outcomes = \(^5C_2*4!*4!= 10*24*24 = 5760\)

Answer: Option A



­Why are you not selecting students for row B? (why do you assume the remaining ones is ok) - something like 5C3 for row B

Could you help Bunuel ?­

­The selection for row B is implicitly covered when selecting for row A. Choosing students for one row automatically determines who will be in the other. After selecting 2 students from 5 for row A, the remaining 3 will be in row B, so you don't need an additional selection step. Or consider this: after selecting 2 students from 5 for row A, there will be 3 students left for row B, so you can say we are selecting 3 out of 3, 3C3, which is 1 way.­
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Re: Eight students were to be seated along two rows such that four student [#permalink]
29 Jul 2024, 00:11
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