Consider the group of 3 dogs as a unit. That means there are 7 friendly dogs, and another "fighting unit" which can be anywhere in the line.
So, there are 8! ways to arrange the dogs which will cause a problem, because the three fighters are all together.
Any other arrangement other than those 8! will be ok. So, there are
10! - 8! ways to line up the dogs so that the three fighters are not together.
I tried so hard for the question below and I couldn't figure it out. Please show some working out. Thanks
10 owners of pedigree dogs will enter the arena to parade their dogs by walking around a circular track. 3 dogs cannot get along together but their is no problem if any 2 of the 3 are together. The number of way avoiding this problem is?
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