seniors&freshmen

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Sun Feb 05, 2012 3:13 pm

In how many different ways can 5 seniors and 3 freshmen be seated in a row of 8 chairs such that the seniors are not separated, and the freshmen are not separated?

A 360
B 720
C 1440
D 2800
E 3200

made up

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Source: Beat The GMAT — Problem Solving | Sun Feb 05, 2012 3:13 pm

[email protected]: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Mon Dec 21, 2009 6:27 am; Location: Melbourne, Australia; Thanked: 17 times

by [email protected] » Sun Feb 05, 2012 4:34 pm

There can be 2 arrangements:
SSSFFFFF
FFFFFSSS
and in each of the above arracgment can be made in 5!x3! ways. So total ways would be=2x360=720.
IMO B

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Sun Feb 05, 2012 4:58 pm

[email protected] wrote:There can be 2 arrangements:
SSSFFFFF
FFFFFSSS
and in each of the above arracgment can be made in 5!x3! ways. So total ways would be=2x360=720.
IMO B

Please explain how you obtained the selection in red?

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[email protected]: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Mon Dec 21, 2009 6:27 am; Location: Melbourne, Australia; Thanked: 17 times

by [email protected] » Sun Feb 05, 2012 7:12 pm

pemdas wrote:
[email protected] wrote:There can be 2 arrangements:
SSSFFFFF
FFFFFSSS
and in each of the above arracgment can be made in 5!x3! ways. So total ways would be=2x360=720.
IMO B
Please explain how you obtained the selection in red?

I miscalculated it earlier as per my logic.
5!x3!=120x6=720.
SO total ways would be 720x2=1440.

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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

by LalaB » Sun Feb 05, 2012 9:31 pm

got the same answer 2!*5!*3!=1440

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Sun Feb 05, 2012 11:25 pm

yes, right
thanks

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