__Category__: Algebra, Statistics"Published in Newark, California, USA"

A passenger train consists of 3 baggage cars, 5 day coaches, and 2 parlor cars. In how many ways can the train be arranged if the 3 baggage cars must come up front?

__Solution__:

The given word problem is about permutation problem because it involves the number of ways in arranging the objects or things.

This permutation type is different and it is called a Distinguishable Permutation.

If a set of n objects consists of k different kinds of objects with n

_{1}, objects of the first kind, n

_{2}objects of the second kind, n

_{3}objects of the third kind, and so on, where n

_{1}+ n

_{2}+ ......... + n

_{k}= n, then the number of distinguishable permutations of these objects is

Now, in the given problem, if

n = 10 train cars in total

n

_{1}= 3 baggage cars

n

_{2}= 5 day coaches

n

_{3}= 2 parlor cars

then, the number of ways in arranging the 10 train cars will be equal to

If the 3 baggage cars must come up front, then the number of ways will be equal to

You have to multiply the previous ways by 3! because the three baggage cars themselves can be arranged in different ways at the front. Therefore, the final answer is