There are (n r) different linear arrangements of n balls of which r are black and n-r are white. give a combinatorial explanation of this fact

Step-by-step explanation:

Combinatorial explanation:

The n balls have to be arranged in n positions and the only distinction is where are the black and where white balls are.

We can choose the position of black balls in ways, therefore, white ones are on the remaining positions.

Using binomial we can have explanation written below:

The balls can be arranged in n! possible permutations.

To be precise one particular arrangement includes permutations. Since r black balls can be permuted in r! ways and white balls in (n-r)! different orders.

So basically it yields,

permutations.

So the actual amount is,

the correct is answer is a 9-sided polygon!