SOLUTION: From a selection of sixteen courses fulfilling a humanities requirement, a student must pick any four to take. How many different combinations of courses are possible?

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Question 1202857: From a selection of sixteen courses fulfilling a humanities requirement, a student must pick any four to take. How many different combinations of courses are possible?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.

The number of all possible different combinations is  C%5B16%5D%5E4 = %2816%2A15%2A14%2A13%29%2F%281%2A2%2A3%2A4%29 = 1820.    ANSWER

Solved.

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Since the order of courses does not matter,  this problem is on  COMBINATIONS.

On  Combinations,  see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.

Learn the subject from there.



Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
c(n,x) is the formul to use.
n is the number of possibe choices.
x is the number of choices to extract from that.
n = 16
4 = x
c(n,x) = n! / (x! * (n-x)!)
when n = 16 and x = 4, the equation becomes c(16,4) = 16! / (4! * 12!) = (16 * 15 * 14 * 13 * 12!) / (4! * 12!) = (16 * 15 * 14 * 13) / (4 * 3 * 2 * 1) = 1820.