Question

8 friends a,b,c,d,e,f,g,h are to be seated in a round table. Find the probability that a and b never sit next to each other/

Answer 1

THE TOTAL NUMBER FRIENDS OF WAY= 8 - 1 = 7

THEREFORE TOTAL NUMBER OF WAY = 6

AGAIN THE SUCH A and B NEVER SIT TOGETHER = 7 -6 = 6 (7-1) = 6*6

THEREFORE THE NUMBER OF FAVOUR ABLE EVENT= 6*6

THUS THE EQUAL PROBABILITY =6*6/7

ANS IS 6/7.

Answer 2

The probability that a and b never sit next to each other is 5/7.

Given,

8 friends a,b,c,d,e,f,g,h are to be seated in a round table.

To find,

Find the probability that a and b never sit next to each other

Solution,

No. of ways 8 people sit in circular table = 7!

No. of way A and B sit together (take A and B as single unit) = 6! x 2

We have to multiply by 2 as A and B can interchange within a unit.

So,

P(a and b never sit next to each other) = 1 - {(6!*2)/7!}

                                                                = 1 - 2/7

                                                                = 5/7

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