The value of - r - 913- rC6 is -

The correct option is B ^14C_7 ^9C_7 ∑ _ r=9 ^ 13 ^rC_6 #160; = ^9C_6+^10C_6+ ^11C_6+ ^12C_6+ ^13C_6 #160; #160; #160; #160; #160; ...

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Byju's Answer

Standard XII

Mathematics

Logarithmic Function

The value of ...

Question

The value of : $13 \sum r = 9^{r} C_{6}$ is :

^{14} C_{7}

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^{14} C_{7} -^{9} C_{7}

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^{13} C_{7} -^{9} C_{7}

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^{13} C_{7} -^{8} C_{7}

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Solution

The correct option is B $^{14} C_{7} -^{9} C_{7}$
$13 \sum r = 9^{r} C_{6} =^{9} C_{6} +^{10} C_{6} +^{11} C_{6} +^{12} C_{6} +^{13} C_{6}$
$=^{9} C_{7} +^{9} C_{6} +^{10} C_{6} +^{11} C_{6} +^{12} C_{6} +^{13} C_{6} -^{9} C_{7}$
$= \frac{9!}{2! 6!} + \frac{9!}{3! 6!} +^{10} C_{6} +^{11} C_{6} +^{12} C_{6} +^{13} C_{6} -^{9} C_{7}$
$= \frac{9!}{2! 6!} [\frac{1}{7} + \frac{1}{3}] +^{10} C_{6} +^{11} C_{6} +^{12} C_{6} +^{13} C_{6} -^{9} C_{7}$
$= {\frac{9! \times 10}{2! \times 6! \times 7 \times 3}}^{10} C_{6} +^{11} C_{6} +^{12} C_{6} +^{13} C_{6} -^{9} C_{7}$
$= \frac{10!}{7! \times 3!} +^{10} C_{6} +^{11} C_{6} +^{12} C_{6} +^{13} C_{6} -^{9} C_{7}$
$=^{10} C_{7} +^{10} C_{6} +^{11} C_{6} +^{12} C_{6} -^{13} C_{6} -_{7}^{C}$
$=^{11} C_{7} +^{11} C_{6} +^{12} C_{6} +^{13} C_{6} -^{9} C_{7}$
$=^{12} C_{7} +^{12} C_{6} +^{13} C_{6} -^{9} C_{7}$
$=^{13} C_{7} +^{13} C_{6} -^{9} C_{7}$
$13 \sum r = 1^{r} C_{6} =^{14} C_{7} -^{9} C_{7}$

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Similar questions

Q. The value of

^{13} C_{7} +^{13} C_{8} +^{13} C_{9} +^{13} C_{10} +^{13} C_{11} +^{13} C_{12} +^{13} C_{13}

A box contains 3 blue, 2 white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will not be a white marble?
(a) $\frac{1}{3}$ (b) $\frac{4}{9}$ (c) $\frac{7}{9}$ (d) $\frac{2}{9}$

Q. If

^{13} C_{r}

is denoted by

C_{r}

, then the value of

C_{1} + C_{5} + C_{7} + C_{9} + C_{11}

is equal to

Q. If

{C_{r}}^{13}

denoted by

C_{r}

then value of

c_{1} + c_{5} + c_{7} + c_{9} + c_{11}

is equal to

Q. The value of

2 \cos \frac{π}{13} \cos \frac{9 π}{13} + \cos \frac{3 π}{13} + \cos \frac{5 π}{13}

is ________________.

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The value of : 13∑r=9rC6 is :

The value of : $13 \sum r = 9^{r} C_{6}$ is :