probability

[Target MA]

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

[MI]

Arranging 5 men around a table = 4!

This creates 5 vacant positions to be filled by women

choose in 3 of them and shuffle = 5c3 x 3!

Total number of ways ( by multiplication rule) = 4! x 5! / 2

[Sumit]

Total no. of ways in which 5 men & 3 women can sit around circular table=7!.

Arranging 5 men around a table = 4!

This creates 5 vacant positions to be filled by women

choose in 3 of them and shuffle = 5c3 x 3!

Total no. of ways in which no two women are adjacent=4!*5c3 x 3!=5!*3!

P(no two women are adjacent)=(5!*3!)/7!=1/7..i.e option a)1/7...

[Target MA]

Total no. of ways in which no two women are adjacent=4!*5c3 x 3!=5!*3!


plz explain this..

[laracroft]

Answer OPTION - C : (2/7)

[Sumit]

Hey Target MA,
Try to Imagine this Suppose If there were only 5 Men then they can be seat in 4! way in a circle now make seat btw all the boys like B_B_B_B_B_ in circle here we have 5 vacant seats for women now we can choose 3 seats from 5 in 5c3 ways and then shuffle three women i.e 3! which will be seated on chosen seats..so final outcome will be 4!*5c3*3!..

@larcroft, How you getting 2/7..????

[laracroft]

Hey Sumit ! You have the right solution .. But on calculating , the answer came out to be 2/7 !!

[Sumit]

My Bad Don't know when my habit for silly mistakes will leave me.....
thanks lara for pointing out....

@Hey Target Ma...Instead Asking for Total no. of ways in which no two women are adjacent=4!*5c3 x 3!=5!*3!...You should have asked why 4!*5c3 x 3!=5!*3!????...I thought you didn't get the solution...