Permutation

For students of class 11-12 (age 16+)
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leonardo shawon
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Permutation

Unread post by leonardo shawon » Sun Jan 16, 2011 1:03 pm

in how many ways N-numbered letters can be arranged where TWO special letters will not be located in first or last of a row...
Ibtehaz Shawon
BRAC University.

long way to go .....

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Moon
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Re: Permutation

Unread post by Moon » Sun Jan 16, 2011 1:29 pm

Fill up the first and the last place at first.
$(n-2) \cdot (n-2) \cdot (n-3) \cdots 2 \cdot 1 \cdot (n-3)=(n-2)(n-3)\cdot (n-3)!$ :)

Edit: Corrected!
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

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HandaramTheGreat
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Re: PERMUTATION

Unread post by HandaramTheGreat » Sun Jan 16, 2011 1:44 pm

আমি পোস্ট লিখে সাবমিট করে দেখি মুন ভাইয়া দিয়া দিল... যাউকগা আমারটাও দিলাম... :)

moon vaia, wouldn't it be $\left( n-2\right) \left( n-3 \right) \left( n-2 \right)!$ ? as repetition isn't allowed... :?
first arrange n letters, then subtract those permutations which have 2 special letters on first or last of the row...
n!-4(n-1)!+2(n-2)!
here 4(n-1)! is those permutations which have at least one letter of those 2 specials in first or last of row... but i've counted the permutations having both letters in first and last twice, so added it...

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Moon
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Re: Permutation

Unread post by Moon » Sun Jan 16, 2011 2:26 pm

Yup...you are right. Actually at first I thought that repetition is allowed...later I edited it, and edited incorrectly. :|
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

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leonardo shawon
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Location: Dhaka

Re: Permutation

Unread post by leonardo shawon » Tue Jan 18, 2011 12:11 pm

moon bhaia,, can u please elaborate? Im not good!
Ibtehaz Shawon
BRAC University.

long way to go .....

HandaramTheGreat
Posts: 135
Joined: Thu Dec 09, 2010 12:10 pm

Re: Permutation

Unread post by HandaramTheGreat » Tue Jan 18, 2011 12:45 pm

first fill up the first place, you can do this in $(n-2)$ ways(you can't consider those 2 special letters), then you can fill up last place in $(n-3)$ ways(as repetition isn't allowed, you have put a letter in first place already)... then $(n-2)$ letters can be arranged in $(n-2)!$ ways...

ok?

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leonardo shawon
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Re: Permutation

Unread post by leonardo shawon » Mon Jan 31, 2011 12:08 am

yaaa.... Thank uu.:)
Ibtehaz Shawon
BRAC University.

long way to go .....

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