Permutations and Combinations
1. 12 applicant remain in the last phase of a scholarship application, where 5 of them are boys and 7 of them are girls. Mr. Lee plans to invite 3 boys and 4 girls for individual interviews next week, 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 3 boys and 4 girls.
(b) The boys should be interviewed successively.
(c) Any two boys should not be interviewed successively.
- 邊位都好Lv 55 年 前最佳解答
1a) 5C3 * 7C4 * 7!= 1764000
1b) 5C3 * 7C4 * 4! * 5C1 * 3!= 252000
1c) 5C3 * 7C4 * 4! * 5C3 * 3!= 504000