Question

In how many ways can 18 white and 19 black balls be arranged in a row so that no two white balls may be together? It is given that balls of the same colour are identical.​

Answer 1

Step-by-step explanation:

we put first black ball make series n put black ball in last no same colour ball r together if not understand see in figure above

hope it helps

Answer 2

The total number of ways are 190.

Step-by-step explanation:

Consider the provided information.

It is given that we have 18 white and 19 black balls.

Now we want no two white balls may be together.

The number of possible ways are:

_B_B_B_B_B_B_B_B_B_B_B_B_B_B_B_B_B_B_B_

Here B represents the black ball and Dash represent the possible places for white ball.

Now we can observe that we have 20 places for white ball.

But we have only 18 white balls.

So number of ways to select 18 white balls from 20 white balls are:

$^{20}C_{18}=\frac{20!}{18!2!}=190$

Hence, the total number of ways are 190.

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