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April 11th, 2008, 06:46 AM  #1 
Newbie Joined: Apr 2008 Posts: 1 Thanks: 0  Permutation or combination??
Hello every one I am a new member and I am happy to join this good forum actually I need your help I have the following problem and I am confused so can you please help me solving it Find the value of x in the following: (a) x = 3nC35 – n + n + 18C3n (b) 10 × x + 3Cx – 2 = x + 3P3 
April 11th, 2008, 09:59 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
What's confusing? How far can you get?

June 5th, 2008, 02:29 PM  #3 
Senior Member Joined: May 2008 From: Sacramento, California Posts: 299 Thanks: 0 
The first one already gives you what x is. I think you might be having trouble because you might be thinking "I need a single number, not a whole expression". But keep in mind you have 4 variables. The first one can be simplified by first multiplying all the numbers of a single term, canceling n's out, and adding together like this: [color=darkred]a) x= 105Cn + 54Cn x= 159Cn That's about as far as it can be simplified.[/color] [color=darkblue]b) 10x + 3Cx – 2= x + 9P (9P=3P3) To isolate x here, you can substract 9P 10x + 3Cx  2  9P= x You can factor this. x= x(10 + 3C)  (2 + 9P) You now substract x(10 + 3C), unfactor, and substract like terms. 9x  3Cx= (2 + 9P) Refactor (again!). I am doing all this factoring and unfactoring to make you see how you can multiply and divide. x(9 + 3C)= (2 + 9P) Divide each side by (9+3C). x= (2 + 9C)/(9 + 3C) x= (2 + 9C)/(9 + 3C) x= (2 + 9C)/3(3+C)[/color] Those would be your values. Can anyone check my answer for me? 

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