F.5 Maths~ :)

JoeyChung

2011-01-15 11:16 pm

John and Mary invite 8 friends to their Christmas Party.Total 10 people.
By the end of the party, the participants are arranged in 2 rows of 5 in order to take a photograph, Find the number of arrangements that can be made if
a.there is no restriction
b.John and Mary are next to each other

回答 (1)

myisland8132

2011-01-15 11:33 pm

✔ 最佳答案

(a) The number of arrangements is just equal to 10! = 3628800. (There is no different between one row and two rows in this case)

(b) First, consider them as a whole and they are at the upper row. Then we need to choose 3 more people from other 8 people with 8C3 choice. In this case the no. of arrangements is equal to (8C3)(4!)(5!). Finally, there are two more factors. (i) we can change the order between John and Mary. (ii) John and Mary can be stood at the lower row. So, the total no. of arrangements is equal to (8C3)(4!)(5!)(2)(2) = 645120

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