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07 May 2025, 02:01
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
52% (02:26) correct
48%
(02:47)
wrong
based on 96
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A motel has 7 different single rooms numbered 1 to 7. The rooms are in situated in a row, in numerical order. There are 5 single guests at the motel one night, Carl, Dan, Emma, Farah and Guy. Dan and Guy are friends and have requested to have rooms with adjacent numbers, however neither of them wants to have room 2. Assuming that their requests are fulfilled, how many different arrangements are there for the guests to be placed in the rooms?
A. 60
B. 120
C. 240
D. 480
E. 960
A. 60
B. 120
C. 240
D. 480
E. 960
02 Jun 2025, 00:10
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Jotting down room numbers for better visualization => 1 2 3 4 5 6 7
As Dan and Guy want to take adjacent rooms, but they don't want to take room no. 2, means they cannot also have room no. 1
Remaining adjacent room pairs are - (3,4) (4,5) (5,6) (6,7)
No. of ways for them to stay in any of this pair = 4C1*2! = 8
After allocating 2 rooms to Dan and Guy, we are left with 5 rooms and 3 guests.
No. of ways to arrange rest of them = 5C3*3! = 60
Combining both the arrangements to get all unique total arrangements = 8*60 = 480
IMO: D
As Dan and Guy want to take adjacent rooms, but they don't want to take room no. 2, means they cannot also have room no. 1
Remaining adjacent room pairs are - (3,4) (4,5) (5,6) (6,7)
No. of ways for them to stay in any of this pair = 4C1*2! = 8
After allocating 2 rooms to Dan and Guy, we are left with 5 rooms and 3 guests.
No. of ways to arrange rest of them = 5C3*3! = 60
Combining both the arrangements to get all unique total arrangements = 8*60 = 480
IMO: D
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Joined: 03 Jun 2023
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02 Jun 2025, 03:38
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1234567 rooms available
D/C dont use room 2 and placed in adjacent rooms hence can only occupy 3/4, 4/5, 5/6, 6/7
Therefore cases possible for D/C accomodation: 4x2!
Now moving to rest of the guests: 3 person being accommodated in 5 rooms makes it: 5C3 x 3!
consequently the answer = (5C3 x 3!) x (4 x 2!) = 480
option D
D/C dont use room 2 and placed in adjacent rooms hence can only occupy 3/4, 4/5, 5/6, 6/7
Therefore cases possible for D/C accomodation: 4x2!
Now moving to rest of the guests: 3 person being accommodated in 5 rooms makes it: 5C3 x 3!
consequently the answer = (5C3 x 3!) x (4 x 2!) = 480
option D
