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A ride at Disneyland can hold 2 people in the front seat and 3 in the

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A ride at Disneyland can hold 2 people in the front seat and 3 in the  [#permalink]

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New post 03 Jul 2018, 01:50
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  25% (medium)

Question Stats:

76% (01:47) correct 24% (01:15) wrong based on 25 sessions

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A ride at Disneyland can hold 2 people in the front seat and 3 in the back seat. A group of 8 friends wish to go on the ride, but since the ride can only hold 5 people at a time, 5 of the friends will go first while the other 3 will wait for the next car. Alice and Stephen will both go in the first group: Alice must sit in the front left seat and Stephen must sit in the back middle seat. In how many ways can the group of 8 friends fill the 5 spots if Alice and Stephen are present in each arrangement?


A. 30

B. 56

C. 90

D. 120

E. 336

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Re: A ride at Disneyland can hold 2 people in the front seat and 3 in the  [#permalink]

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New post 03 Jul 2018, 06:43
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Bunuel wrote:
A ride at Disneyland can hold 2 people in the front seat and 3 in the back seat. A group of 8 friends wish to go on the ride, but since the ride can only hold 5 people at a time, 5 of the friends will go first while the other 3 will wait for the next car. Alice and Stephen will both go in the first group: Alice must sit in the front left seat and Stephen must sit in the back middle seat. In how many ways can the group of 8 friends fill the 5 spots if Alice and Stephen are present in each arrangement?


A. 30

B. 56

C. 90

D. 120

E. 336


2 of 8 friends are already decided to go in first ride and their positions also are already fixed so we only need 3 more individuals out of remaining 6 for the first ride

3 out of 6 for teh first ride can be selected in 6C3 = 20 ways
Those selected 3 in first ride can be seated in 3! ways

i.e. first ride may be taken in 6C3*3! = 30*6 = 120 ways

Answer: Option D

Bunuel: the language of the question seems misleading because it asks at the end "i each arrangement" so it might mean that Alice and Stephen are going in second ride as well. Please check and see If I am making sense.
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Re: A ride at Disneyland can hold 2 people in the front seat and 3 in the &nbs [#permalink] 03 Jul 2018, 06:43
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