Expert: Soroban - 9/12/2007

Question
My son received a math problem that I could not figure. There are 7 different train cars. How many combinations can you make that would be pulled by the the engine train? There must be some kind of formula to solve this equation at a 3rd grade level. Thank you- Carlos

Answer
Hello, Carlos!

This is quite tricky for 3rd grade.

There are 7 different cars.
    Call them: A, B, C, D, E, F, G  if you like.

I'll assume we want to make 7-car combinations for the train
   and the order of the cars makes difference.
For example:  ABCDEFG is considered different from BCDEFGA


For the first car, we have 7 choices (any of the 7 cars).

Once we pick the first car, there are 6 choices for the second car.

Then there are 5 choices for the third car.
And 4 choices for the fourth car.
Then 3 choices for the fifth car.
And 2 choices for the sixth car.
And there's 1 car left for the seventh car.

The number of combinations is the PRODUCT of these choices.

There are:  7 × 6 × 5 × 4 × 3 × 2 × 1  =  5,040 different combinations.
.