Question

In a train yard there are 4 tank cars, 12 boxcars, and 7 flatcars. How many ways can a train be made up consisting of 2 tank cars, 5 boxcars, and 3 flatcars if their order make no difference.

Answer 1

Answer: Correct answer is 4,151,347,200

Step-by-step explanation:

I did the assignment.

Answer 2

Answer:

The trian can be made up in 166,320 ways.

Step-by-step explanation:

The order makes no difference, which means that we use the combinations formula to solve this problem.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

We are going to choose

2 tank cars from a set of 4

5 boxcars from a set of 12

3 flatcars from a set of 7

How many ways can a train be made up?

Multiplication of the number of possibles sets of tanks, boxcars and flatcars. So

$T = C_{4,2}*C_{12,5}*C_{7,3} = \frac{4!}{2!2!}*\frac{12!}{5!7!}*\frac{7!}{3!4!} = 6*792*35 = 166320$

The trian can be made up in 166,320 ways.