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8 person stand in line at random.what is the probability the two persons X and Y donot stand together
Asked by c65118124 | 17 Jan, 2024, 03:18: PM

To arrange 8 persons in a line , number N of possible ways is

N = 8 !

If X and Y stand together , let us say X first and Y next, then there are 7 ways they can can stand somewhere in a line.

Remaining 6 places can be filled by  ( 6 ! ) ways .

If the order of X any reversed , i.e. Y first and X next , then there are another 7 ways they can stand together and

remaining places are filled by ( 6 ! ) ways.

Hence total number of possible ways in which X any Y are together is  ( 2 × 6! × 7 ) ways = 2 × 7! ways

Hence probability p( X and Y ) of X and Y are standing together is

Hence probability p( not X and Y together )  = 1 - (1/4) = 3/4

Answered by Thiyagarajan K | 17 Jan, 2024, 04:54: PM

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