Combination- how to arrange balls

David99

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May 16, 2019
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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?
 
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.
 
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