# Combination- how to arrange balls

#### David99

##### New member
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? In how many ways can the balls be arranged if no red ball is next to a white?

#### pka

##### Elite Member
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? In how many ways can the balls be arranged if no red ball is next to a white?
Here are two ways: $$\displaystyle RRR\boxed{RBW}WW~\&~WW\boxed{WBR}RRR$$
Are there others?
Please show some effort.