Algebraic Solving for perms/combs

[K.ourt]

Yea..we got one example in our notes, and looking back it doesnt seem to explain a thing. Grar. Anyways, any hints or help would be amazing, since I dont seem to grasp this concept.

1) nP2=30. And I know this can be re-written as n!/(n-2)!=30, but from there Im rather lost.

2)nC2=15. I know it can be re-written as n!/((n-2)!2!). But yea..


And I know both the questions have an answer of (or at least one of the answers is) 6 because I guessed and checked.

 

[galactus]

Think of what a factorial is.

n!=n(n-1)(n-2)(n-3)(n-4)....................

(n-2)!=(n-2)(n-3)(n-4).......................

Since you have \(\displaystyle \frac{n!}{(n-2)!}\)

Everything cancels but n(n-1). See?.

n(n-1)=30, solve for n.

 

[pka]

You must understand the recursive definition of factorial.
Study these.
\(\displaystyle \L
\begin{array}{rcl}
n! & = & n(n - 1)! \\
n! & = & n(n - 1)(n - 2)! \\
\frac{{n!}}{{(n - 2)!}} & = & n(n - 1) \\
\end{array}\)

\(\displaystyle {n \choose 2} = \frac {n!} {(n-2)! (2!)} = \frac {n(n-1)} {2}\)