Question 284028: How many ways are there to select 3 books from a shelf of 20 books?
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! If order matters, then there are 20 ways to select the first book, 19 to select the second, and 18 to select the third (since we're not replacing the books). Multiply these values to get 20*19*18 = 6840
So there are 6840 different ways to select 3 books from a shelf of 20 where order matters.
If order does NOT matter, then you will have duplicates to worry about. It turns out that each triple (ie each selection of 3) occurs 6 times. For instance, if you have books 'a', 'b', and 'c', then you will have the following:
abc
acb
bac
bca
cab
cba
Notice there are 6 ways to order 'a', 'b', and 'c'
If order does NOT matter, then you must divide the previous result of 6840 by 6 to get 1140. Dividing by 6 will eliminate the counting of duplicates. So there are 1140 different ways to select 3 books from 20 where order does NOT matter.
Formally, we just computed the permutation of 20 choose 3 for the first answer and a combination of 20 choose 3 for the second.
Answer by solver91311(24713)  (Show Source):
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