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Question

The sum of the series
2 20C0+5 20C1+8 20C2+11 20C3++62 20C20
is equal to:

A
224
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B
225
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C
223
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D
226
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Solution

The correct option is B 225
2 20C0+5 20C1+8 20C2+11 20C3++62 20C20
=(30+2)20C0+(31+2)20C1+(32+2)20C2 +1(33+2)20C3++(320+2)20C20=20r=0(3r+2)20Cr=320r=0r20Cr+2220
=320r=0r(20r) 19Cr1+221=60219+221=225

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