• Apr 4th 2010, 04:32 PM
sweeetcaroline
Please help! I'm not really sure how to start solving this problem. A parking lot has 18 spaces in a row. 10 cars arrive, each of which requires one parking space and their drivers choose their spaces at random from among the available spaces. Auntie Em then arrives in her SUV, which requires 2 adjacent spaces. What is the probability that she is able to park?
• Apr 4th 2010, 05:00 PM
Plato
You need to find out how many ways to arrange ten 1’s and eight 0’s in such a way that no two 0’s are adjacent.
• Apr 4th 2010, 07:26 PM
Anonymous1
Quote:

Originally Posted by Plato
You need to find out how many ways to arrange ten 1’s and eight 0’s in such a way that no two 0’s are adjacent.

Following what Plato suggested...

We place the ones such that,

1_1_1_1_1_1_1_1_1 $\color{red}{1}$

Notice $\color{red}{1}$ is the only $"1"$ that does not have to be fixed. and it can be in $1$ of the $9$ possible available spaces.

Therefore the probability she $can't$ find a spot is...
• Apr 4th 2010, 08:38 PM
Soroban
Hello, sweeetcaroline!

Am I reading the problem correctly?

Quote:

A parking lot has 18 spaces in a row. 10 cars arrive, each requiring one parking space.
Their drivers choose their spaces at random from among the available spaces.

Auntie Em then arrives in her SUV, which requires two adjacent spaces

What is the probability that she is able to park?

We are parking ten normal cars: . $\blacksquare\;\blacksquare\;\blacksquare\;\blacksq uare\;\blacksquare\;\blacksquare\;\blacksquare\;\b lacksquare\;\blacksquare\;\blacksquare$

. . and one SUV: . $\blacksquare\!\blacksquare$

After the ten cars are parked randomly, what is the probabiity
. . that there is at least a pair of adjacent empty spaces?