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Question

nr = 1nCr is

A
2n
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B
2n + 1
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C
2n - 1
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D
2n1
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Solution

The correct option is C 2n - 1
nr = 0nCr = nC0 + nC1 +nC2 + ... + nCn = 2nnr = 1nCr = nC1 +nC2 + ... + nCn Add and subtract nC0 on RHSnr = 1nCr = nC0 + nC1 +nC2 + ... + nCn nC0 = 2n 1

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