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Greatest Binomial Coefficients

Maximum value...

Question

Maximum value of $^{15} C_{r}$ is

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Solution

Maximum value of $^{15} C_{r} :$
Here, $15$ is odd $^{15} C_{r}$ will be maximum when $r = \frac{n - 1}{2} = \frac{14}{2} = 7$ or
$r = \frac{n + 1}{2} = \frac{16}{2} = 8$
$\Rightarrow^{15} C_{7} =^{15} C_{8} = 6435$

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Similar questions

(^{15} C_{r} +^{15} C_{r - 1}) (^{15} C_{15 - r} +^{15} C_{16 - r}) = (^{16} C_{13})^{2}

, then the value of

r

^{15} C_{3 r} =^{15} C_{r + 3}

, then the value of r is:

Q. The value of

\sum_{r = 1}^{15} r^{2} (\frac{^{15} C r}{^{15} C r - 1})

^{15} C_{3 r} =^{15} C_{r + 3}

, then find the value of

r

:

^{15} C_{r} :^{15} C_{r} = 11 : 5

r

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Greatest Binomial Coefficients

Standard XII Mathematics

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