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In how many different ways can 10 students of a class with roll number
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07 Jan 2022, 02:52
07 Jan 2022, 02:52
Expert Reply
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Question Stats:
75% (02:01) correct
25% (02:29) wrong based on 12 sessions
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In how many different ways can 10 students of a class with roll numbers from 1 to 10 be seated in a straight line such that one of the extreme positions has a student with an odd roll number while the other extreme position has a student with an even roll number?
(A) 48 × 6!
(B) 44 × 12!
(C) 50 × 8!
(D) 50 × 6!
(E) 52 × 8!
Kudos for the right answer and explanation
See more at this link GRE Tips and Tricks - UPDATED 11/20/2021
(A) 48 × 6!
(B) 44 × 12!
(C) 50 × 8!
(D) 50 × 6!
(E) 52 × 8!
Kudos for the right answer and explanation
See more at this link GRE Tips and Tricks - UPDATED 11/20/2021
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In how many different ways can 10 students of a class with roll number
[#permalink]
07 Jan 2022, 06:02
07 Jan 2022, 06:02
2
Carcass wrote:
In how many different ways can 10 students of a class with roll numbers from 1 to 10 be seated in a straight line such that one of the extreme positions has a student with an odd roll number while the other extreme position has a student with an even roll number?
(A) 48 × 6!
(B) 44 × 12!
(C) 50 × 8!
(D) 50 × 6!
(E) 52 × 8!
Kudos for the right answer and explanation
See more at this link GRE Tips and Tricks - UPDATED 11/20/2021
(A) 48 × 6!
(B) 44 × 12!
(C) 50 × 8!
(D) 50 × 6!
(E) 52 × 8!
Kudos for the right answer and explanation
See more at this link GRE Tips and Tricks - UPDATED 11/20/2021
There are two possible cases:
case i: ODD _ _ _ _ _ _ _ _ EVEN
5 options for 1st position
5 options for 10th position
8 options for 2nd position
7 options for 3rd position
6 options for 4th position
.
.
.
2 options for 8th position
1 option for 9th position
TOTAL = (5)(5)(8)(7)(6)....(3)(2)(1)
= (25)(8!)
case ii: EVEN _ _ _ _ _ _ _ _ ODD
5 options for 1st position
5 options for 10th position
8 options for 2nd position
7 options for 3rd position
6 options for 4th position
.
.
.
2 options for 8th position
1 option for 9th position
TOTAL = (5)(5)(8)(7)(6)....(3)(2)(1)
= (25)(8!)
GRAND TOTAL = (25)(8!) + (25)(8!) = (50)(8!)
Answer: C
General Discussion
Re: In how many different ways can 10 students of a class with roll number
[#permalink]
15 Jun 2024, 13:48
15 Jun 2024, 13:48
1
There are 5 odd numbers and 5 even numbers from 1 to 10 so first slot will take 5 for odd and last slot will take 5 for even
Second slot will take 8 and so on
5x8x7x6x5x4x3x2x1x5
But there are 2 of such possibilities so
5x8x7x6x5x4x3x2x1x5x2
Which will give 50x8!
Answer C
Adewale Fasipe, GRE, GMAT quant instructor from Lagos, Nigeria.
Second slot will take 8 and so on
5x8x7x6x5x4x3x2x1x5
But there are 2 of such possibilities so
5x8x7x6x5x4x3x2x1x5x2
Which will give 50x8!
Answer C
Adewale Fasipe, GRE, GMAT quant instructor from Lagos, Nigeria.
