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The 6 seats across the front row of an aeroplane are labeled A to F. 26 Oct 2021, 03:45
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25% (medium)

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73% (01:33) correct 27% (01:47) wrong based on 226 sessions

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The 6 seats across the front row of an aeroplane are labeled A to F. The seats labeled “A” and “F” are window seats. The 4 members of the Rourke family, including a baby, are being seated in these 6 seats. Given that the baby must be given a window seat, and the family must sit in adjacently lettered seats, how many different possible seating arrangements are there for the family?


(A) 6

(B) 12

(C) 48

(D) 60

(E) 120
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The 6 seats across the front row of an aeroplane are labeled A to F. 26 Oct 2021, 05:03
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Given that the baby must be given a window seat, and the family must sit in adjacently lettered seats

If baby chooses seat A, the family can sit in (3 x 2 x 1) 6 different ways.
If baby chooses seat F, the family can sit in (3 x 2 x 1) 6 different ways.

Total ways = 6 + 6 = 12
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The 6 seats across the front row of an aeroplane are labeled A to F. 27 Oct 2021, 01:25
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Made a terrible mistake here. Did not see "including".
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The 6 seats across the front row of an aeroplane are labeled A to F. 12 Nov 2022, 22:30
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though question is simple but having tough times with this.
gmatophobia

i have attached my approach to solve this question . please help me
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The 6 seats across the front row of an aeroplane are labeled A to F. 12 Nov 2022, 23:12
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AnujL
though question is simple but having tough times with this.
gmatophobia

i have attached my approach to solve this question . please help me
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Hi AnujL

You're correct in identifying that the baby can take either seat A or can take seat F. However, that's just one of the criteria.

Now let's see what other information is given to us.

  • The family must sit in adjacently lettered seats

Inference: All the members of the family should be together.

Question: How many different possible seating arrangements are there for the family?

Inference: The word, arrangements, indicates us that seating position does matter. Hence the questions is regarding permutation and we need to consider the order of each member.

Now let's proceed solving the question, we know that the baby will either occupy seat A or seat F. So we can fix the position of the baby and then find out which seats the other members of the family can occupy.

A B C D E F

Say the baby is at position A - The other members of the family must occupy position B C D, and in these position they can be seated in seat in 3! ways.

A B C D E F

Say the baby is at position F - The other members of the family must occupy position C D E, and in these position they can be seated in 3! ways.

So total number of arrangements = 2 * 3! = 2 * 6 = 12

Option B

A side note :
You have considered that the order won't matter, but in fact the order does matter as the question is about arrangement.

Hope this answers.
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The 6 seats across the front row of an aeroplane are labeled A to F. 15 Oct 2024, 12:42
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