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Question

The sum of series 20C020C1+20C220C3+....+20C10 is

A
20C10
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B
1220C10
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C
0
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D
20C10
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Solution

The correct option is A 1220C10
(1+x)20=20C0+20C1x+....+20C10x10+....+20C20x20

Put x=1

0=20C020C1+...20C9+20C1020C11+.....+20C20

0=2(20C020C1+....20C9)+20C10

20C10=2(20C020C1+....20C9+20C10)

20C020C1+....+20C10=12 20C10

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