Question 204463: In how many ways can 6 instructors be assigned to six sections of a course in mathematics?
I can not do word problems can you please explain this to me... I really need help...
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! If in doubt, think small. Let's say that we wanted to know many many ways 3 instructors can teach 3 different courses. We'll call the teachers 'a', 'b', and 'c'. Also, the order of these letters matters. So abc is different from cba. Here are ALL the possible ways you can order the three letters:
abc, acb, bac, bca, cab, cba
Note: acb means that teacher 'a' teaches the first course, 'c' does the second, and 'b' does the third
From this list, we can see that there are 6 possible combinations.
Now what if we don't want to list out EVERY combination (the number of combinations may be quite large)? We could use the counting principle
The idea is this: you have 3 slots (for the three courses) and you have 3 choices for the first slot, 2 for the second (since one is already taken for the first one) and finally you have one choice left over. You simply take the values in those slots and multiply them out. In other words, you have
Slot one*Slot two*Slot three
now plug in the given values to get:
3*2*1 = 6
So you're basically taking the given value 3 and you are multiplying it by every number until you reach 1. This is shortened to use the factorial notation. So 
In your case, you want to evaluate  . I'll let you calculate out the final answer. I hope my explanation made a little sense.
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