Combinations

👨🏻‍🏫 學術台數學

Vincent Wong

2007-11-27 5:51 am

What's the number of combinations that
1)putting n different books into r same boxes;
2)putting n same books into r same boxes;
3)putting n same books into r different boxes;
4)putting n different books into r different boxes.

更新1:

both n and r are positive integers

更新2:

to freda_yeung: exactly wrong...

更新3:

one box can contain ∞ books

回答 (1)

用戶46949

2007-11-27 11:54 pm

✔ 最佳答案

Assume n > r , and one box can only contains one book
1) n! / [(n-r)! ( r)! ]
2) one combination
3) one combination
4) n! / (n-r)!

2007-11-27 16:19:21 補充：
Assume n 〈 r , and one box can only contains at most one book or no book1) one combination2) one combination3) r ! / [(r-n)! (n) !] 4) r ! / (r-n) !

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