# Combinatorics/Permut/Solv Eqs Involving Factorial Notation.

• Mar 16th 2009, 10:07 AM
AGrondin
Combinatorics/Permut/Solv Eqs Involving Factorial Notation.
Hey any help with the following would be much appreciated:

Solve for n where:

P (n,5)=42 * P (n,3)

based on the fact C(n,r)=n!/(n-r)r! , I got:

n!/(n-5)!5!=42* n!/(n-3)!3!

, is this the right step to start? if not, why not? and what would be the proper solution to this problem???
• Mar 16th 2009, 11:43 AM
Plato
Quote:

Originally Posted by AGrondin
Solve for n where:
P (n,5)=42 * P (n,3) based on the fact C(n,r)=n!/(n-r)r!?

Problem: $\displaystyle P(n,r)=\frac{n!}{(n-r)!}$..
You are using combinations to do permutations.
• Mar 16th 2009, 12:05 PM
AGrondin
yes I believe so, any suggestions/help to offer?
Thanks
• Mar 16th 2009, 12:19 PM
Plato
This my point, you are using he wrong formula.
$\displaystyle \frac{n!}{(n-5)!}=42\cdot\frac{n!}{(n-3)!}$
• Mar 16th 2009, 12:38 PM
AGrondin
That would leave me with (n-3)(n-4)=42 leaving me with n=10, n=-3 therefore n=10 ?