What is the probability that if Paul, Mary, and Susan are in a group of 7...

What is the probability that if Paul, Mary, and Susan are in a group of 7 people randomly seated in 7 chairs, they want to be in consecutive chairs. What is the probability if the chairs are set in a circle?

Expert Solution

First of all, 7 people can sit in 7 chairs in 7! ways. I dont think i have to explian this.

Next, if we want Paul, Mary and Susan tom sit together , we may think them as one unit. So, we have to arrange sits for this one unit ansd the remaining 4 people. which can be done in (4+1)! = 5! ways.

Now, inside this group of three, they can arrange themselves in 3! ways.

So, no of favourable cases : 5! *3!

So, probability that, the 3 people sit together =

In case of circular arrangement, 7 people can sit in 7 seats in (7-1)! = 6! ways.

JUSTIFICATION: In a circular arangement, position of the chairs are identical , so when we make the 1st person sit, there is only 1 effective choice. and remaining 6 can be arranged in 6! ways. thus 6! .

and if we want the 3 people to sit together, choice ill be = 3! * (5-1)! = 3! * 4!

So, probability =

If you have doubts, or having trouble let me know below. Thanks

milcah answered 1 year ago

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