Mahi and Parth are in a line with 6 other people.what is the probability that they are exactly three places away from each other ?

Question

Probability question

Answer 1

Let's show all possible arrangements containing Mahi (M) and Parth (P) along with 4 other warm bodies (o).

 

M o o P o o -- P is 3 places away from M (by virtue of there being precisely two others between them.

o M o o P o

o o M o o P

P o o M o o

o P o o M o

o o P o o M

 

That's six ways that satisfy the particular criterion that is required.

There are 6! possible arrangements, without any restrictions (ordered permutations).

 

My answer: 6/6! = 1/5! = 1/ (5•4•3•2•1) =1/ 120.

 

The above last line was corrected to fix omission of numerator (1)