A and B stand in a ring with 10 other persons. if the arrangement of the twelve persons is at random ; Find the chance that there are exactly 3 persons between A and B .
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Fixing A and B on desired places
There are three places in between that can be filled in 10c3 ways
The rest places are 7 that can be filled in
10c7 ways
So the ways are 10c3×10c7
But we can sift A and B in one more way
Thus the total ways are
2×10c3×10c7
There are three places in between that can be filled in 10c3 ways
The rest places are 7 that can be filled in
10c7 ways
So the ways are 10c3×10c7
But we can sift A and B in one more way
Thus the total ways are
2×10c3×10c7
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5
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