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Question

The expression nCr+n-1Cr+.........+rCr is equal to :


A

n+1Cr

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B

n+1Cr+1

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C

n+2Cr

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D

2n

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Solution

The correct option is B

n+1Cr+1


Explanation For The Correct Option

Evaluating the expression

The Given expression:

nCr+n-1Cr+.........+rCr

nCr+n-1Cr+n-2Cr+......+r+2C+(r+1Cr+r+1Cr+1)

We know that n+1Cr+1=nCr+1+nCr

nCr+n1Crn+n2Cr+......+r+2Cr+r+2Cr+1

nCr+n1Crn+n2Cr+......+r+3Cr+1

By continuing this, we get

nCr+n-1Cr+n-1Cr+1nCr+nCr+1n+1Cr+1

Hence, the correct answer is Option (B),


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