probab

[kogo]

Five Men and three women are to sit around a circular table. If they chose their positions at a
random. What is the probability that no two women are adjacent
a) 1/7 c) 2/7
 b) 1/9 d) 2/9

[Sumit]

c)2/7

[Akshay Jain]

2/7

[kogo]

how?

[Akshay Jain]

total no. of possible arrangements = (n-1)! (circular permutations) = 7!
total no. of ways in which 5 boys can be arranged at alternate positions = 5!
there are total 5 positions left among boys in which 3 girls have to be seated so that no two girls are together= 5P3
requared probability= 5!*5P3/7!=2/7

[Sinistral]

first arrange 5 men around the circular table.
they can be arranged in (5-1)! = 4! ways.

Now 5 chairs can be put in between those 5 men arranged (hence men and women will sit alternatively).
this can be done by choosing 3 chairs (places) out of those 5 chairs (places) and arranging 3 women in those 3 selected chairs (places) . this can be done in 5C3*3! ways (or simply 5P3 ways).

Hence no. of ways in which the given arrangement can be made = 4! * 5P3

total no. of ways of arranging those 5 men + 3 women (8 people) = 7!.

so required Pr = [4! * 5P3] / 7! = 2/7

[Akshay Jain]

correction to above ans...
initially 5 boys can be arrenged at alternate positions in 4! ways (circle)
so ans is 4!*5P3/7!=2/7...:P

[kogo]

thank you :)