permutation

2010-10-15 8:51 am

1. There are 10 successive parking spaces in a car park. 7 cars are going to park into these spaces. If it is required that the 3 unoccupied spaces are next to eah other,in how many ways can the spaces be assigned to the cars?

2. There are 8 members in a swimming club. To participate in a medley relay,a team of four members will be selected to swim in butterfly,backstoke,breaststroke and freestyle respectively. It is known that three members of the club cannot swim in butterfly only and the others are able to swim in any stroke. Find the number of ways of forming the swimming team.

Thanks!

回答 (1)

用戶2053

2010-10-16 9:10 am

✔ 最佳答案

1)3 unoccupied spaces are next to eah other :10 - 3 + 1 = 8 ways ,For each ways , 7 cars have 7! ways to park ,8 * 7! = 40320 ways.
2)
Selecte 1 member among 5 members who are able to swim in any stroke to
swim in butterfly first ,5P1 = 5 waysThen selecte 4 members among others 7 members to swim in backstoke,breaststroke and freestyle ,7P3 = 210 ways 5 * 210 = 1050 ways.

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