Question

x=16cr at what value r does the minimum and maximum value of x occur

Answer 1

maximum -> r=8
minimum-> r=0,16

Answer 2

Answer:

The value of x is minimum at r=0 and r=16. The value of x is maximum at r=8.

Step-by-step explanation:

If a combination is defined as

$^{n}C_r$

Then the value of this combination is minimum at r=0 and r=n. The value of this combination is maximum at r=n/2 (when n is even) and r=(n+1)/2 (when n is odd).

The given equation is

$x=^{16}C_r$

Here n=16, which is an even number.

It means the value of x is minimum at r=0 and r=16.

$x=^{16}C_0=^{16}C_{16}=1$

The value of x is maximum at r=8.

$x=^{16}C_8=\frac{16!}{8!(16-8)!}=12870$

Therefore, the value of x is minimum at r=0 and r=16. The value of x is maximum at r=8.