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

^{n + 4} C_{r}

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

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^{n} c_{r}

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11.

^{n} c_{r}

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Solution

The correct option is D $^{n + 4} C_{r}$
$^{n} C_{r} + 4.^{n} C_{r - 1} + 6.^{n} C_{r - 2} + 4^{n} C_{r - 3} +^{n} C_{r - 4}$
$=^{4} C_{0} .^{n} C_{r} +^{4} C_{1} {.1}^{n} C_{r - 1} +^{4} C_{2} .^{n} C_{r - 2} +^{4} C_{3} .^{n} C_{r - 3} +^{4} C_{4} .^{n} C_{r - 4}$
$=^{n + 4} C_{r}$

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Similar questions

^{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} + 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}

k

\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}

\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} + {2.}^{n} C_{r - 1} +^{n} C_{r - 2} =^{n + 2} C_{r}

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