Multinomial probability confusion The probabilities are $0.4$, $0.5$, and $0.1$ that, in a city driving, a certain compact car will average less than $22$ miles per gallon, from $22$ to $26$ miles per gallon, or more than $26$ miles per gallon. Find the probability that among $10$ such cars tested, $3$ will average $22$ miles per gallon, $6$ will average $22$ to $26$ miles per gallon, and $1$ will average more than $26$ miles per gallon.
I know we should multiply the probabilities, $(0.5)^{6}$ and such, to the cars we are choosing, but how exactly to choose the cars I am confused. 
EDIT: I do not want the formula as I already know it exists. I want an argument that counts what the question is asking for. 
Can anyone give me a hint on how to get started? I'm writing things down on paper, but it doesn't get me anywhere.

We have $10$ cars. We run each car and test its mpg. Each car fall into a slot with a certain probability, and so occupies one digit of $4444555551$.
So after $10$ cars have been tested, we have a string such as $1555414554$.
The number of the strings of this form is given by:
$$\dfrac{10!}{6!3!1!}$$
and the probability for each digit to occur is:
$$(0.4)^3, (0.5)^6, (0.1)^1$$
