Question

In how many ways 5 white and 4 black balls be arranged ina row so that no two blacks balls are together?

Answer 1

In 15 ways, 5 white and 4 black balls be arranged in a row so that no two black balls are together.

Step-by-step explanation:

There are 5 white and 4 black balls.

First, we arrange 5 white balls.

_W_W_W_W_W_

After arrangement of 5 white balls, there are 6 places in which we have to arrange black balls so that no two black balls are together.

There are 6 places and we have to arrange 4 black balls.

Number of ways to arrange 4 black balls in 6 places = $6_{C_{4} }$ = $\frac{6\times 5 \times 4! }{2!\times 4!} = \frac{6\times 5}{2}$

                                                                                        = 15 ways

Hence, in 15 ways 5 white and 4 black balls be arranged in a row so that no two black balls are together.