Maths F5 (Permutation) 4題

2012-09-10 3:06 am

1.) There are 9 cubic blocks marked with different numbers. 5 of them are blue and the
rest are pink. Maggie puts all the blocks in a row. Find the number of permutations if no
pink blocks are put next to each other.

2.) Pauline has 1 dictionary, 1 comic and 5 different fictions. She wants to put 4 books on
the lower shelf and 3 books on the upper shelf. If the dictionary and the comic are put in
different shelves, find the number of arrangements of the books.

3.) 6 children are arranged to sit in a row. And each one raises one hand before a teacher
takes a photo of them. In how many ways can the children be arranged to sit with each one raising one hand?

4.) Christine is preparing for the examinations of five subjects: Chinese,
English, Mathematics, Liberal Studies and Physics. She plans to study one subject each
day from Monday to Friday and no subjects are repeated in these five days. In how many
ways can the subjects be arranged if she must study Physics on Monday and must not
study English on Friday?

回答 (1)

50418129

2012-09-11 6:59 pm

✔ 最佳答案

(1)

5 blue blocks have 5P5 ways to put in a row
there are then 6 gaps for 4 pink blocks to put, i.e. 6P4 ways
so, there are 5P5 x 6P4 ways in total

(2)

case i, dictionary on top and comic at the bottom
choose 1 dictionary and choose 2 fictions form 5 on the top and have
1C1 x 5C2 x 3P3 ways to put in row
choose 1 comic and choose 3 fictions form the other 3 at the bottom and have
1C1 x 3C3 x 4P4 ways to put in row
case i, comic on top and dictionary at the bottom
similar to case i,
so, there are 1C1 x 5C2 x 3P3 x 1C1 x 3C3 x 4P4 x 2 ways in total

(3)

don't understand the question, may you translate in chinese?

(4)

Physics on Monday, 1P1 way
English not on Friday means Chinese, Math or LS on Friday, 3P1 ways
others on Tuesday, Wednesday and Thursday, 3P3 ways
so, there are 1P1 x 3P1 x 3P3 ways in total

參考: knowledge

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