Another simple probability question

If people are seated in a random manner in a row containing seats, what is the probability that no two people will occupy adjacent seats?

__My solution__:

There are favourable arrangements.

__Total no. of arrangements__:

The 1st person can sit on any of the seats, the 2nd person can sit on any of the other seats and so on. So, the number of ways to seat people on seats is .

But the answer given in the book is . Where have I gone wrong?

Re: Another simple probability question

Quote:

Originally Posted by

**alexmahone** If

people are seated in a random manner in a row containing

seats, what is the probability that no two people will occupy adjacent seats? the answer given in the book is

.

Think of a string of *n* zeros and *n* ones.

There are ways to arrange that string.

The *n* zeros create *n+1* spaces to put the ones so that no two ones are together.

EXAMPLE: *n=4*, "_0_0_0_0_" that is five places.

Thus places seat the *n* people no two together.

which is the book's answer.

Re: Another simple probability question

The first person can sit on any of 2n seats but the second person cant sit in next seat so doesnt have a choice of 2n-1 seats.

Re: Another simple probability question

Quote:

Originally Posted by

**biffboy** The first person can sit on any of 2n seats but the second person cant sit in next seat so doesnt have a choice of 2n-1 seats.

Actually, I was counting the total number of arrangements.