SOLUTION: I do understand the relationship between nPr and nCr {( nPr = r!(nCr) } and all. But I am missing something with the following that obviously should be apparent! How does (nP5)

Algebra ->  Permutations -> SOLUTION: I do understand the relationship between nPr and nCr {( nPr = r!(nCr) } and all. But I am missing something with the following that obviously should be apparent! How does (nP5)       Log On


   

Question 1164375: I do understand the relationship between nPr and nCr {( nPr = r!(nCr) } and all. But I am missing something with the following that obviously should be apparent!
How does (nP5) translate into nP4 X (n-4) in the following expression given in the book:
30(nP5/5!) = [30 X nP4 X (n-4)] / 5!
Can somebody show me the intermediate steps...just with the translation of nP5 to as nP4 X (n-4)
Also I am new to this site. How do I insert subscripts in the equations while posting the questions?
Thank you
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Must be a misprint.  They aren't equal:

30%28%22nP5%22%2F5%21%29+=+%2830%2A%22nP4%22%2A%28n-4%29%29%2F5%21

By definition:

%22nP5%22+=+n%28n-1%29%28n-2%29%28n-3%29%28n-4%29%28n-5%29
%22nP4%22+=+n%28n-1%29%28n-2%29%28n-3%29%28n-4%29

So nP5 just has one more factor, (n-5), than nP4 has,

So nP5 = (n+5)nP4.

The misprint in your book was that the (n-4) on the right should have been (n-5).

Books have typos sometimes.

Edwin