Posted by **Samir** on Tuesday, January 22, 2008 at 7:12pm.

1:A train is to consist of three flatcars, five tankers, six boxcars, an engine and a caboose.In how many ways can the train be made ?

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**Damon**, Tuesday, January 22, 2008 at 8:26pm
I will assume engine up front and caboose at the rear so the different ways relate to the other cars.

Now we do not know if the tankers are all picked up together and the flatcars together etc. or not. In practice that would be likely because they would come from different places, so I will assume that you have a group of 3, a group of 5 and a group of 6

Now those three groups can be arranged in 3! = 6 ways

If it does not matter what order the cars are in within the groups, you are finished. However if it does, we need to go on.

The permutations of 3 is 3! = 6

of 5 is 5! = 120

of 6 is 6! = 720

so we have the original 6 for the three groups times all the permutations within the groups

6*6*120*720

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