Identify if this is a combination or permutation and then answer the questions.
Aaron has 6 autographed baseballs and room for 4 in his display case. How many arrangements can he make?

Question

Identify if this is a combination or permutation and then answer the questions.
Aaron has 6 autographed baseballs and room for 4 in his display case. How many arrangements can he make?

experimentx · Answer

does it matter how he put it in order???

sburchette · Answer

This would be a combination because the order wouldn't matter; at least, that is what I am assuming.  Having baseballs 1,2,3, and 4 would be the same as having baseballs 4,3,2, and 1, for example.  So we a combination of 6 items taken 4 at a time or 6C4. The formula for a combination is $$(n!)/(r!(n-r)!)$$ where n is the total and r is the amount taken at a time. Substituting 6 for n and 4 for r we get $$(6!)/(4!(6-4)!)$$ Which simplifies to $$(6!)/(4!*2!)$$ This gives us 15. So there are 15 combinations he can make with 6 cards taken four at a time if the order doesn't matter.