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Question

Question: <sup>n</sup>C<sub>r–1</sub> + 3 <sup>n</sup>C<sub>r</sub> + 3 <sup>n</sup>C<sub>r+1</sub> + <sup>n</...

nCr–1 + 3 nCr + 3 nCr+1 + nCr+2 is equal to

A

n+2Cr+1

B

n+2Cr+2

C

n+2Cr+3

D

n+3Cr+2

Answer

n+3Cr+2

Explanation

Solution

nCr–1 + nCr + 2(nCr + nCr+1) + nCr+1 + nCr+2

= n+1Cr + 2 n+1Cr+1 + n+1Cr+2

= n+1Cr + n+1Cr+1 + n+1Cr+1 + n+1Cr+2

= n+2Cr+1 + n+2Cr+2 = n+3Cr+2