"Minor defects are found on $7$ of $10$ new cars. If $3$ of the $10$ cars are selected at random, what is the probability that $2$ have minor defects?"
I don't understand why "$3C1 = 3$ ways of choosing $1$ non defective car of $3$" must be calculated to solve this problem. Can you explain?
From Barron's SAT Subject Test Math 2 book
Best Answer
When you choose 3 cars at random where 2 cars are defective, you could have chosen the cars in the different possible orders
Defective car, Defective car, Good Car
or
Good Car, Defective car, Defective car
or
Defective car, Good Car, Defective car
There are three positions for the good car.
So if you pick 4 cars at random with 3 defective cars you could have
$_4C_3$ ways to choose.