Question

prove That,

n^Cr-1 + 2n^Cr-2 + n^Cr-3 = n+2^Cr-1


___________
chp: Permutation and combination.


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Answer 1

Answer:

Step-by-step explanation:

Here, we will use the property of binomial coefficients,

nCr+nCr−1=(n+1)Cr

L.H.S.=nCr+2⋅nCr−1+nCr−2

=nCr+nCr−1+nCr−1+nCr−2

Using the above property,

=(n+1)Cr+(n+1)Cr−1

Again using the above property,

=(n+2)Cr=R.H.S.