First slide

Combinations

Question

If n is even and $^{n} C_{0} <^{n} C_{1} <^{n} C_{2} < \dots <^{n} C_{r} >^{n} C_{r + 1} > \dots >^{n} C_{n}$ then r =

Moderate

A

$\frac{n}{2}$
B

$\frac{n - 1}{2}$
C

$\frac{n - 2}{2}$
D

$\frac{n + 2}{2}$

Solution

By the given condition, it is clear that $^{n} C_{r}$ is the greatest among $^{n} C_{0},^{n} C_{1}, \dots,^{n} C_{n}$ .
Since n is even,
$∴^{n} C_{r} is the greatest for r = \frac{n}{2}$
$∴ r = \frac{n}{2}$

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