Quod Erat Demonstrandum

2011/01/07

Exercise in counting balls and boxes

Filed under: Additional / Applied Mathematics,HKALE,NSS — johnmayhk @ 7:43 上午
Tags:

The following is just a basic counting exercise from a secondary mathematics textbook (used in Taiwan, I guess), enjoy.

Find the number of ways of

1. placing 5 distinguishable balls into 7 distinguishable boxes (answer) (solution);

2. placing 5 distinguishable balls into 7 indistinguishable boxes (answer) (solution);

3. placing 5 indistinguishable balls into 7 distinguishable boxes (answer) (solution);

4. placing 5 indistinguishable balls into 7 indistinguishable boxes (answer) (solution);

5. placing 5 distinguishable balls into 7 distinguishable boxes such that every box contains at most 1 ball (answer) (solution);

6. placing 5 indistinguishable balls into 7 distinguishable boxes such that every box contains at most 1 ball (answer) (solution);

7. placing 7 distinguishable balls into 5 distinguishable boxes such that every box contains at least 1 ball (answer) (solution);

8. placing 7 distinguishable balls into 5 indistinguishable boxes such that every box contains at least 1 ball (answer) (solution);

9. placing 7 indistinguishable balls into 5 distinguishable boxes such that every box contains at least 1 ball (answer) (solution);

10. placing 7 indistinguishable balls into 5 indistinguishable boxes such that every box contains at least 1 ball (answer) (solution).

It may be fun to select questions which are suitable in the NSS syllabus in Hong Kong.

Gook luck.

P.S. The solutions are not given in the book, refine my solutions if you think they are ugly, thanks!

2 則迴響 »

  1. john sir第十題的答案出錯哦,那應該是placing 7 indistinguishable balls into 5 indistinguishable boxes such that every box contains at least 1 ball 的答案。
    答案應該係7C3+7C2X5C2/2=140

    迴響 由 jaychan — 2011/01/07 @ 12:43 下午 | 回覆

    • Oops, 打錯了題目,改了,thank you for debugging!

      迴響 由 johnmayhk — 2011/01/07 @ 12:48 下午 | 回覆


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