1. In how many ways can 4 red balls, 3 white balls and 1 black ball be arranged in a line so that the black ball is always surrounded by a red and a white ball?

2. In how many ways can the balls be arranged if no red ball is next to a white?

Thank you in advanced.

For 1) 'glue a red ball to the black ball then 'glue' a white to the other side of the black ball.

How many ways can the block of three along with the remaining three red balls & two white balls (six units in all) be arranged?

Now for 2) here are two correct strings:

\(\displaystyle r\,r\,r\,r\,b\,w\,w\,w\text{ Or }w\,w\,w\,b\,r\,r\,r\,r\)

Is there any other possible strings?