Question

How many different trains can you make of length three?

Answer 1

Using the combination formula, and supposing that you have n parts, it is found that the number of trains you can make is of:

$N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}$

The order in which the parts are taken is not important, hence the combination formula is used to solve this question.

What is the combination formula?

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

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

In this problem, 3 parts are taken from a set of n, hence the total number of trains is given by:

$N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}$

More can be learned about the combination formula at brainly.com/question/25821700

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