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Question

The value of (21C110C1)+(21C210C2)+(21C310C3)+(21C410C4)++(21C1010C10) is:

A
221211
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B
221210
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C
22029
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D
220210
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Solution

The correct option is D 220210
(21C1 10C1)+(21C2 10C2)+(21C3 10C3)++(21C10 10C10)
=(21C1+ 21C2++ 21C10)(10C1+ 10C2++ 10C10)

Now, 21C1+ 21C2++ 21C10
=12(21C1+ 21C2++ 21C10+ 21C1+21C2++ 21C10)
=12(21C1+ 21C2++ 21C10+ 21C20+21C19++ 21C11)
=12(2212)=2201

10C1+ 10C2++ 10C10
=2101

Required sum =220210

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