SOLUTION: Dear math teacher, Would you help me explain how to convert r! to r? Here is the problem I am talking about: Given nPr=3024 and nCr=126, find r. nCr=nPr/(r!) 126=30

Algebra ->  Permutations -> SOLUTION: Dear math teacher, Would you help me explain how to convert r! to r? Here is the problem I am talking about: Given nPr=3024 and nCr=126, find r. nCr=nPr/(r!) 126=30      Log On


   

Question 475581: Dear math teacher,
Would you help me explain how to convert r! to r?
Here is the problem I am talking about:
Given nPr=3024 and nCr=126, find r.
nCr=nPr/(r!)
126=3024/(r!)
r!=24
Here is where I get stuck because I don't know how to take factorial to an integer. The textbook's answer lists r=4 as an answer but I do not understand how they converted r! to r. Would you please explain it to me?
Thank you very much for your help and time.
Sincerely,

I.
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since 4! = 4*3*2*1 = 24, this means that if r%21=24, then r=4


If this isn't familiar, then I suggest using a table or a calculator.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
nPr/nCr=r! --> r!= 3024/126= 24 --> r=4 ....--> r!=24=4*3*2*1=4!
nC4= 126 --> n·(n-1)·(n-2)·(n-3)/24= 126 --> n·(n-1)·(n-2)·(n-3)= 3024
--> n=9 it is a solution