Combination- how to arrange balls

David99

New member
Joined
May 16, 2019
Messages
2
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
Joined
Jan 29, 2005
Messages
8,128
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.
 
Top