Eight friends go to watch a movie but only 5 tickets were

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BTGmoderatorLU: Moderator; Posts: 2650; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Tue Mar 05, 2019 2:36 pm

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Source: Veritas Prep

Eight friends go to watch a movie but only 5 tickets were available. In how many different ways can 5 people sit and watch the movie?

A. 8C5
B. 8*7*6*5*4
C. 5!
D. 8!/5!
E. 8*5

The OA is B

Source: Beat The GMAT — Problem Solving | Tue Mar 05, 2019 2:36 pm

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Wed Mar 06, 2019 1:38 am

I don't like the wording of the question, because it's not altogether clear if order should matter. But that's the intention, so we have 8 choices for which person goes in the first seat, 7 for the next seat, and so on, and multiplying our choices gives the answer of (8)(7)(6)(5)(4).

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Mar 08, 2019 6:50 am

BTGmoderatorLU wrote:Source: Veritas Prep

Eight friends go to watch a movie but only 5 tickets were available. In how many different ways can 5 people sit and watch the movie?

A. 8C5
B. 8*7*6*5*4
C. 5!
D. 8!/5!
E. 8*5

The OA is B

This is a permutation problem because the seating order is important. The number of ways for 8 friends to sit and watch a movie to which only 5 of them can obtain an admission ticket is 8P5 = 8 x 7 x 6 x 5 x 4.

Answer: B

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