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:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
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
[tex]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[/tex]
The trian can be made up in 166,320 ways.
The number of ways is 166,320ways
If there are "n" objects, the number of ways of selecting r objects is expressed as:
If there are 4 tank cars, 12 boxcars, and 7 flatcars in a train yard, the number of ways a train be made up consisting of 2 tank cars, 5 boxcars, and 3 flatcars is expressed as:
Hence the number of ways is 166,320ways
Learn more on combination here: https://brainly.com/question/9465501
