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GRE Practice Question for January 20th

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? 

Incorrect. Did you use the combination formula instead of the permutation formula?

Incorrect. You made two errors: using the combination formula and not accounting for the two people who must be seated first.

Incorrect. Did you accidentally multiply 6 x 5 x 3? There are 120, not 90, total arrangements.

This is the credited response. There are 120 ways to seat the 6 remaining people in the 3 remaining spots.

Did you use n = 8 and k = 5? Remember that two of the 8 people must be seated first.

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