SOLUTION: If C(n,3)=C(n,4),then the value of n?????please help me to solve this problem.

Algebra ->  Permutations -> SOLUTION: If C(n,3)=C(n,4),then the value of n?????please help me to solve this problem.      Log On


   

Question 989699: If C(n,3)=C(n,4),then the value of n?????please help me to solve this problem.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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C(n,3)=n!/(3!(n-3)!)
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C(n,4)=n!/(4!(n-4)!)
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n!/(3!(n-3)!)=n!/(4!(n-4)!) Divide each side by n!
1/(3!(n-3)!)=1/(4!(n-4)!) Cross multiply
3!(n-3)!=4!(n-4)! Divide each side by 3!
(n-3)!=4(n-4)! Divide each side by (n-4)!*(Note below)
n-3=4(1)
n-3=4
n=7
ANSWER: n=7
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*NOTE: (n-3)!=(n-3)(n-4)! so (n-3)!/(n-4)!=(n-3)
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CHECK:
n!/(3!(n-3)!)=n!/(4!(n-4)!)=
7!/(3!(7-3!))=7!/(4!(7-4)!)=
7!/(3!4!)=7!/(4!3!)
(7*6*5)/(3*2*1)=(7*6*5)/(3*2*1)
210/6=210/6
35=35