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Arrangement

by Naruto » Sun Jun 14, 2009 4:30 am
In how many ways can 15 students be seated in a row so that 2 most talkative children never sit together.

A 14! 14!
B 15.14!'
C 14!
D 14!.13
E 15!


Shouldnt the answer be 14.14!

I mean 15 students can be arranged in 15! ways and assuming that 2 most talkative always sit together. 14! ways, hence the ways in which they never sit together 15!-14! = 14! (15-1) = 14.14!. What am i doing wrong?
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by Neo2000 » Sun Jun 14, 2009 7:21 am
Total number of ways = 15!

Consider the 2kids as 1 unit, they can now be arranged in 14! x 2! since the two kids can be arranged among themselves in 2! ways

Hence answer = [spoiler]13.14![/spoiler]
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by ssmiles08 » Sun Jun 14, 2009 7:34 am
I am getting 15! - (2*14!) which i guess is like Neo2000 said 14!*13
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by Naruto » Sun Jun 14, 2009 7:51 am
ssmiles08 wrote:I am getting 15! - (2*14!) which i guess is like Neo2000 said 14!*13
Right I missed the 2. got it thanks!
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