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Question

Find the value of 1000C500+1000C501


A

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B

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C

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D

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Solution

The correct option is D


nCr+nCr1=n+1Cr
Here, n=1000 and r=501
1000C500+1000C501=1001C501
Explanation for the result:
nCr+nCr1=n!(nr)!×r!+n!(n(r1))!×(r1)!
= n!(nr)!×(r1)!(1r+1(n(r1)))
= n!(nr)!×(r1)!(nr+1+r)(n(r1)×r)
= (n+1)n!(nr)!×(n(r1)(1r(r1)!)
= (n+1)!(nr+1)!(1r!)
= n+1Cr


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