# Permutation.......

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• Mar 24th 2008, 12:19 AM
micmac63
Permutation.......
Hi all, need some help here,

Simplify

2n+2
. .Pn
2n
. .Pn

thanks
• Mar 24th 2008, 01:45 AM
mr fantastic
Quote:

Originally Posted by micmac63
Hi all, need some help here,

Simplify

2n+2
. .Pn
2n
. .Pn

thanks

Simplify $\frac{^{2n+2}P_n}{^{2n}P_n}$.

Do you know that $^n P_r = \frac{n!}{(n-r)!}$ ?
• Mar 24th 2008, 01:58 AM
micmac63
yes, but dont quite understand ?????
• Mar 24th 2008, 02:03 AM
mr fantastic
Quote:

Originally Posted by mr fantastic
Simplify $\frac{^{2n+2}P_n}{^{2n}P_n}$.

Do you know that $^n P_r = \frac{n!}{(n-r)!}$ ?

Quote:

Originally Posted by micmac63
yes, but dont quite understand ?????

$\frac{^{2n+2}P_n}{^{2n}P_n} = \frac{\frac{(2n+2)!}{(2n+2-n)!}}{\frac{(2n)!}{(2n-n)!}} = \frac{\frac{(2n+2)!}{(n+2)!}}{\frac{(2n)!}{n!}} = \frac{(2n+2)!}{(n+2)!} \times \frac{n!}{(2n)!} = .....$
• Mar 24th 2008, 02:31 AM
micmac63
Thankyou so much, Im helping my daughter with this, and she is on right track now,

if the equation equals 3.5, find the value of n ?

thanks again.
• Mar 24th 2008, 03:41 AM
mr fantastic
Quote:

Originally Posted by micmac63
Thankyou so much, Im helping my daughter with this, and she is on right track now,

if the equation equals 3.5, find the value of n ?

thanks again.

Solve $\frac{(2n+2)(2n+1)}{(n+2)(n+1)} = \frac{7}{2} \Rightarrow 2(2n+2)(2n+1)=7(n+2)(n+1) .....$

Expand both sides and re-arrange into the form:

quadratic = 0.

Solve this equation in the usual way, noting the restriction $n \geq 0$.

For checking purposes: n = 10.