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Bunuel
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Eric and Ortega and their teammates watch a movie. They all sit in a 17 Apr 2019, 21:27
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B
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74% (01:06) correct 26% (02:01) wrong based on 201 sessions

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Eric and Ortega and their teammates watch a movie. They all sit in a row, and they can sit in n different ways. In how many of the ways can Eric sit to the right of Ortega?

(A) n
(B) n/2
(C) n/3
(D) n/4
(E) n/5
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B
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Eric and Ortega and their teammates watch a movie. They all sit in a 18 Apr 2019, 03:26
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Bunuel
Eric and Ortega and their teammates watch a movie. They all sit in a row, and they can sit in n different ways. In how many of the ways can Eric sit to the right of Ortega?

(A) n
(B) n/2
(C) n/3
(D) n/4
(E) n/5
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total arragement ; n
both sit together so n/2 possible ways
IMO B
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Eric and Ortega and their teammates watch a movie. They all sit in a 29 Aug 2019, 17:32
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Archit3110
Bunuel
Eric and Ortega and their teammates watch a movie. They all sit in a row, and they can sit in n different ways. In how many of the ways can Eric sit to the right of Ortega?

(A) n
(B) n/2
(C) n/3
(D) n/4
(E) n/5

total arragement ; n
both sit together so n/2 possible ways
IMO B
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Archit3110

Why do we assume that they are going to be seated together if we do not know know many teammates are there also?

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Eric and Ortega and their teammates watch a movie. They all sit in a 30 Aug 2019, 10:37
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VeritasKarishma Bunuel
Can you please help with the explanation?

Posted from my mobile device
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Eric and Ortega and their teammates watch a movie. They all sit in a 30 Aug 2019, 10:40
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They are not necessarily seated together - the solution above that says they are is incorrect.

If you seat the group of people randomly, half the time Eric will be to the right of Ortega, and half the time Eric will be to the left of Ortega. So if there are n seating arrangements in total, there must be n/2 seating arrangements in which Eric is somewhere to the right of Ortega.
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Eric and Ortega and their teammates watch a movie. They all sit in a Updated on: 30 Nov 2023, 06:20
Originally posted by KarishmaB on 31 Aug 2019, 02:23.
Last edited by KarishmaB on 30 Nov 2023, 06:20, edited 1 time in total.
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himanshurajawat
VeritasKarishma Bunuel
Can you please help with the explanation?

Posted from my mobile device
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This post discusses this concept:
https://anaprep.com/combinatorics-linea ... -symmetry/
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Eric and Ortega and their teammates watch a movie. They all sit in a 09 Sep 2019, 10:55
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Bunuel
Eric and Ortega and their teammates watch a movie. They all sit in a row, and they can sit in n different ways. In how many of the ways can Eric sit to the right of Ortega?

(A) n
(B) n/2
(C) n/3
(D) n/4
(E) n/5
Show more

We should notice that for any arrangement where Eric sits to the left of Ortega, if we switch the positions of Eric and Ortega and keep everyone else fixed, we will obtain an arrangement in which Eric sits to the right of Ortega. Thus, the number of arrangements where Eric is to the right of Ortega is equal to the number of arrangements in which Eric is to Ortega’s left. Since the total number of arrangements is n, the total number of ways in which Eric can sit to Ortega’s right is n/2.

Answer: B
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Eric and Ortega and their teammates watch a movie. They all sit in a 03 Apr 2025, 21:07
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