## Permutation

For students of class 11-12 (age 16+)
leonardo shawon
Posts: 169
Joined: Sat Jan 01, 2011 4:59 pm
Location: Dhaka

### Permutation

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 .....

Moon
Posts: 751
Joined: Tue Nov 02, 2010 7:52 pm
Contact:

### Re: Permutation

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

learn how to write equations, and don't forget to read Forum Guide and Rules.

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

### Re: PERMUTATION

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...

Moon
Posts: 751
Joined: Tue Nov 02, 2010 7:52 pm
Contact:

### Re: Permutation

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

learn how to write equations, and don't forget to read Forum Guide and Rules.

leonardo shawon
Posts: 169
Joined: Sat Jan 01, 2011 4:59 pm
Location: Dhaka

### Re: Permutation

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

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?

leonardo shawon
Posts: 169
Joined: Sat Jan 01, 2011 4:59 pm
Location: Dhaka

### Re: Permutation

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

long way to go .....