permutations (5m)

用戶90882

2010-08-06 10:33 pm

Consider the knowledge of permutations, please help me to answer the questions.

1. There are 5 boys and 4 girls. Now these 9 students are arranged in a row, find the number of permutations if girls are arranged at both ends.

Q1 Solutions: 60 480

2. Which of the following cases will give the same number of permutations? Explain briefly.

Case 1: 6 people are arranged in one row.

Case 2: 6 people are arranged in two rows, where there are 2 people in the first row and 4 in the second row.

Case 3: 6 people are arranged in two rows, where there are 2 people in one row and 4 in the other row.

Q2 Solutions: Case 1 and case 2

Thank you. 5 marks

回答 (1)

用戶2053

2010-08-06 10:47 pm

✔ 最佳答案

1)2 girls at both ends : 4P2 = 12 cases ,5 boys and 2 girls between 2 girls at both ends : 7! = 5040 casesTotal 5040 * 12 = 60 480 cases.
2)Case 1: 6 people are arranged in one row. 6! = 720
Case 2: 6 people are arranged in two rows, where there are 2 people in the first row and 4 in the second row. (1st row 2 from 6)(2nd row 4 from 4) (6P2)(4P4) = 30 * 24 = 720

Case 3: 6 people are arranged in two rows, where there are 2 people in one row and 4 in the other row.(1st row 2 from 6)(2nd row 4 from 4) + (1st row 4 from 6)(2nd row 2 from 2)(6P2)(4P4) + (6P4)(2P2) = 1440 ways
Case 1 = Case2 = 720

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