Q1 of 118 Page 17

Write in the simplified form.

We know:


nCr + nCr-1 = n+1Cr ⇒ (1)


n+rCr = nC0 + n+1C1 + n+2C2 + n+3C3 + . . . . . . + n+mCn+1


n+rCr = n+1C0 + n+1C1 + n+2C2 + n+3C3 + . . . . . . + n+mCn+1 ⇒ (nC0 = n+1C0)


Using equation (1),


n+rCr = n+2C1 + n+2C2 + n+3C3 + . . . . . . + n+mCn+1


n+rCr = n+3C2 + n+3C3 + . . . . . . + n+mCn+1


Proceeding in the same way :


n+rCr = n+mCm-1 + n+mCm = n+m+1Cn+1


n+rCr = n+m+1Cn+1


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