Help with Combinatoric problem.
You need to put your reindeer, Rudy, Ezekiel, Gloopin, Bloopin, and Prancer, in a single-file line to pull your sleigh. However, Bloopin and Rudy are fighting, so you have to keep them apart, or they won't fly.
How many ways can you arrange your reindeer?

Question

hartnn · Answer

The number of ways to arrange 'n' objects is n!


what have you tried?

hartnn · Answer

Hint: The number of way in which those 2 reindeers are apart 
 = Total number of ways - The number of ways in which those 2 reindeers are always together.

Because,
'The number of ways in which those 2 reindeers are always together' is easier to find.

knov · Answer

I found out the total number of ways to arrange all reindeers. Which is 5!.

knov · Answer

and then i calculated the number of ways to arrange those two are together. which is 12. and somehow it's incorrect.

hartnn · Answer

5! is correct.

Now, for those 2 to be always together, 
firstly consider them to be the ONE. 

so, there will be 4! ways, right?

secondly, consider re-arranging those 2 among themselves, 2! ways.

so in all, 4!*2! ways.

does this make sense?

knov · Answer

Yeah, now I got it. Thanks for the help.

hartnn · Answer

welcome ^_^