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The sum i=0m. 10Ci×20Cmi where pCq=0 if p<q is maximum, when m is

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a
5
b
10
c
15
d
20

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detailed solution

Correct option is C

We have, ∑i=0m 10Ci×20Cm−i= Number of ways of selecting m objects from two groups of objects one group containing 10 distinct objects of one type and another group containing 20 distinct objects of second kind.=30CmClearly,  30Cm is maximum when m=15, because  nCr is maximum for r=n/2 if n is even and when n is odd it ismaximum for r=n+12 or n−12.


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