SOLUTION: 18Cr=18C(r+2). what is the value of rC5?

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Question 636760: 18Cr=18C(r+2). what is the value of rC5?
Answer by sachi(548) About Me  (Show Source):
You can put this solution on YOUR website!
18Cr=18C(r+2)
or 18!/[r!(18-r)(18-r-1)(18-r-2)!]=18!/[(r+2)(r+1)r!(18-r-2)!]
simplifying we get
(r+2)(r+1)=(18-r)(18-r-1)
or r^2+3r+2=324-36r-18+r^2+r-18=r^2-35r+306
or 38r=306-2=304
or r=304/38=8
so rC5=8C5=8!/5!(8-5)!=8*7*6/3*2*1=56 ans