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Question

The value of (7C0+7C1)+(7C1+7C2)+...+(7C6+7C7)


A

271

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B

282

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C

281

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D

28

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Solution

The correct option is B

282


(7C0+7C1)+(7C1+7C2)+(7C2+7C3)+(7C3+7C4)+(7C4+7C5)+(7C5+7C6)+(7C6+7C7)

=1+2×7C1+2×7C2×7C3+2×7C4+2×7C5+2×7C6+1

=1+2×7C1+2×7C2×7C3+2×7C3+2×7C2+2×7C6+1

=2+22(7C1+7C2+7C3)

=2+22(7+72×6+73×62×5)

=2+252=254

=282


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