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You are creating your highschool schedule and you get to pick what times you take each class. You have Geometry, Earth Science, English Literature, Ancient History and Music Appreciation. You have 7 class periods to choose from. How many different ways can you arrange your schedule?
21

35

5

2520

Question

Fan And medal
You are creating your highschool schedule and you get to pick what times you take each class. You have Geometry, Earth Science, English Literature, Ancient History and Music Appreciation. You have 7 class periods to choose from. How many different ways can you arrange your schedule?
   21
 
   35
 
   5
 
   2520

kohai · Answer

So with these, you just multiply all of the classes by all of the times to find all the possible combinations

mathmate · Answer

The way to look at the problem is you have 5 subjects and two free periods (total 7) for each of the classes.
There are 7 choices for the first class, 6 for the second, and so on.  These numbers are to be multiplied together to get the number of choices.
Since the two free periods are identical, we have to divide the previous result by two to get the number of unique choices.