Number of participants

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alex.gellatly: Master | Next Rank: 500 Posts; Posts: 435; Joined: Wed Nov 16, 2011 7:27 am; Thanked: 48 times; Followed by:16 members

Number of participants

by alex.gellatly » Sat Jul 28, 2012 11:04 pm

Each participant in a certain study was assigned a sequence of 3 different letters form the set {A,B,C,D,E,F,G,H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study? (Note, A,B,C is different from C,B,A.)

20
92
300
372
476

I got the correct answer, just putting it out there for different approaches. Enjoy.

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Source: Beat The GMAT — Problem Solving | Sat Jul 28, 2012 11:04 pm

Birottam Dutta: Master | Next Rank: 500 Posts; Posts: 342; Joined: Wed Jul 08, 2009 8:50 am; Thanked: 214 times; Followed by:19 members; GMAT Score:740

by Birottam Dutta » Sat Jul 28, 2012 11:15 pm

Lemme have a crack at it.

Since order matters, it must be permutation.

Now, 3 letters can be selected from 8 in 8P3 ways = 336 ways.

Since 36 possible sequences are not assigned to any participant,

Number of distinct participants = 336-36 = 300.

Hope this is correct!

Answer C!

Folks please check this out
https://www.youtube.com/watch?v=H7p56NzAVKc

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alex.gellatly: Master | Next Rank: 500 Posts; Posts: 435; Joined: Wed Nov 16, 2011 7:27 am; Thanked: 48 times; Followed by:16 members

by alex.gellatly » Sun Jul 29, 2012 7:25 pm

Birottam Dutta wrote:Lemme have a crack at it.

Since order matters, it must be permutation.

Now, 3 letters can be selected from 8 in 8P3 ways = 336 ways.

Since 36 possible sequences are not assigned to any participant,

Number of distinct participants = 336-36 = 300.

Hope this is correct!

Answer C!

You got it