Based on this information answer the questions given below.
(i) $^{n} C_{p} = r!^{n} C_{r}$
(ii) $^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r}$
What is the value of $^{8} C_{4} +^{8} C_{3}$ ?

^{8} c_{5}

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63

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35

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^{9} c_{4}

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Solution

The correct option is D $^{9} c_{4}$
$^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r}$
$\Rightarrow^{8} C_{4} +^{8} C_{3} =^{9} C_{4}$

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Similar questions

^{n} C_{r - 1} = 36,^{n} C_{r} = 84

^{n} C_{r + 1} = 126

^{r} C_{2} = 8

^{n} C_{r} =^{n} C_{n - r}

S = \sum_{r = 0}^{n} \frac{3^{r + 4} ({^{n} C}_{r})}{{^{r + 4} C}_{4}} + \sum_{r = 0}^{3} \frac{{^{n + 4} C}_{r} 3^{r}}{{^{n + 4} C}_{4}}

\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 \geq r - 1

{^{n} C}_{r - 1} + {^{n + 1} C}_{r - 1} + {^{n + 2} C}_{r - 1} + . . . . + {^{2 n} C}_{r - 1} = {^{2 n + 1} C}_{r^{2} - 182} - {^{n} C}_{r}

n

n

r

^{n} C_{r - 1} :^{n} C_{r} :^{n} C_{r + 1} = 20 : 35 : 42

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