Solve the following

Question:

The value of nCr + 2 nCr – 1 + nCr – 2, 2 ≤ r ≤ n, is ____________.

Solution:

nCr + 2nCr−1 + nCr−2 

nCr + nCr−1 + nCr−1 nCr−2 

n+1Cr + n+1Cr−1 

n+2C using identity  

∴ nCr + nCr−1 nCr−2 = n+2C2

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