In how many ways can 6 ppl be seated in a circle if 2 ppl are always separated.
Two girls have their birthdays in the same week.It is known that one
of the girls was born on a saturday. determine the prob that both
were born on a saturday.
Let me try ....
The total number of ways in which N people can be seated in a circle = (N - 1)!
If two people (say A and B) are next to each other, the remaining (N-2) people can be arranged in (N-2)! ways - in one direction and (N-2)! more ways in the other direction i.e. 2*(N-2)! ways
So, answer = (N - 1)! - 2*(N-2)! = 5! - 2*4! = 120 - 48 = 72
I think this can be generalized to say that of N people, 2*(N-t)! ways exist in which t of N are next to one another, where t < N and (N-1)! - 2*(N-t)! ways exist in which t of N people are not next to one another.
Am I right?
Is the answer 1/7 for the second one?
Given that the two girls were born in the same week, the probability will be 1 of the seven days.