There are 9 cars and 9 parking spaces in a row. If 3 sport cars are randomly in the group of 9 cars, what is the probability that the sports cars are parked in a row?
For this question is found the number of ways the sports cars can be parked in a row in 9 spots. They can be parked in 7*6 different ways out of a possible 9!.. correct?
So i had 42/362880=.00011574
Doesnt this seem a little low?
Hello, mathlete2!
Another approach . . .
There are 9 cars and 9 parking spaces in a row.
If 3 sport cars are randomly in the group of 9 cars,
what is the probability that the sports cars are adjacent?
There are: . possible arrangments.
Duct-tape the 3 sports cars together.
. . Then there are 7 "cars" to arrange: .
There are: . permutations.
But the 3 sports cars can be permuted in ways.
Hence, there are: . ways for the sports cars to be adjacent.
Therefore, the probability is: .