1708Thanks hsbhatt sir.....(crystal clear explanation.)
find all positive integer value of n and r that satisfy the equation C(n , r) = 2010..
(hsbhatt sir how can i solve these tupe of question).
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2 Answers
341This is similar to an olympiad problem whose solution I had read before.
2010 = 2 \ \times \ 3 \times \ 5 \ \times 67
It is obvious that we must have n \ge 67
We need to consider only r≤n/2 (Since nCr=nCn-r)
Now if r≥2, then \binom {n}{r} \ge \binom {n}{2} \ge \binom {67}{2} = 2211>2010
Hence r =1 giving n=2010.
So the only solutions are (2010,1) and (2010,2009)