Permutations and Combinations

1997年7月1日

2014-01-27 1:01 pm

1.
There are 6 mobile phones (P1, P2, P3, P4, P5, P6) from Brand P and 5 mobile phones (Q1, Q2, Q3, Q4, Q5) from Brand Q. If they are placed in one row, find the number of permutations according to each of the following conditions.
(a) Q1 and Q2 must be placed next to each other.
(b) Q1 and Q2 must not be placed next to each other.
(c) Any two mobile phones from Brand Q must not be placed next to each other.

2.
12 applicants remain in the last phase of a scholarship application, where 7 of them are boys and 5 of them are girls. Mr. Wong plans to invite 4 boys and 3 girls for individual interviews next month, and thus he is going to make a list according to the ordering of interviews. Find the possible number of lists to be made according to each of the following conditions.

(a) Select any 4 boys and 3 girls.
(b) The girls should be interviewed successively.
(c) Any two girls should not be interviewed succesively.

Thank you very much!

回答 (1)

少年時

2014-01-27 6:31 pm

✔ 最佳答案

1a. Set Q1, Q2 as a group, so it seems there are 10 phones,No. of ways = 2! * 10!
1b. All the ways except part 1a is ok.No. of ways = 11! - 2! * 10!
1c. Arrange Brand P first : 6!Then there are 7 ways to place Brand Q, ie. P(7, 5). No. of ways = 6! * P(7,5)

2a. No. of ways to select any 4 boys is C(7,4),and no. of ways to select any 3 girls is C(5,3).So the total possible number of list = C(7,4) * C(5,3) * 7!
2b. Set all the girls as a group, similar to part 1a,Total possible ways = C(7,4) * C(5,3) * 3! * 5!
2c. Similar to part 1b,Total possible ways = C(7,4) * C(5,3) * 4! * P(5,3)

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