If nCr-3nCr-1-3nCr-2-nCr-3-nCr-4nCr-1-6nCr-2-4nCr-3-nCr-4-r-k-n-k- then the value of k equals

The correct option is B 4 ^nC_r+3^nC_r+1+3^nC_r+2+^nC_r+3/^nC_r+4^nC_r+1+6^nC_r+2+4^nC_r+3+^nC_r+4 =r+k/n+k ⇒ #160;r+4/n+4=r+k/n+k ⇒ ...

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Properties of Iota

If nCr+3nCr...

Question

If $\frac{^{n} C_{r} + 3^{n} C_{r + 1} + 3^{n} C_{r + 2} +^{n} C_{r + 3}}{^{n} C_{r} + 4^{n} C_{r + 1} + 6^{n} C_{r + 2} + 4^{n} C_{r + 3} +^{n} C_{r + 4}} = \frac{r + k}{n + k}$ , then the value of $k$ equals

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\frac{^{n} C_{r} + 4^{n} C_{r + 1} + 6^{n} C_{r + 2} + 4^{n} C_{r + 3} +^{n} C_{r + 4}}{^{n} C_{r} + 3^{n} C_{r + 1} + 3^{n} C_{r + 2} +^{n} C_{r + 3}} = \frac{n + k}{r + k}

^{n + 4} C_{r} -^{n} C_{r} - {3.}^{n} C_{r - 1} - 3^{n} C_{r - 2} -^{n} C_{r - 3}

\frac{^{n} C_{r}}{^{n} C_{r + 1}} = \frac{1}{2}

\frac{^{n} C_{r + 1}}{^{n} C_{r + 2}} = \frac{2}{3}

n

r

^{n} C_{r} + {4.}^{n} C_{r - 1} + {6.}^{n} C_{r - 2} + {4.}^{n} C_{r - 3} +^{n} C_{r - 4} =

(2 \leq r \leq n),

^{n} C_{r} + 2 \cdot^{n} C_{r + 1} +^{n} C_{r + 2}

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