SOLUTION: Eight people are to form two queues of four. In how many ways can this be done if: a) there are no restrictions, b) Jim will only stand in the left hand queue, c) Sean and Liam

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Question 1131922: Eight people are to form two queues of four. In how many ways can this be done if:
a) there are no restrictions,
b) Jim will only stand in the left hand queue,
c) Sean and Liam must stand in the same queue?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Eight people are to form two queues of four. In how many ways can this be done if:
a) there are no restrictions,
There are 8 different positions to place the 8 people.

Answer: 8! = 40320

b) Jim will only stand in the left hand queue,
Half of the 40320 positions Jim will be in the left hand queue
and half in right hand queue.

Answer: 40320÷2 = 20160

c) Sean and Liam must stand in the same queue?
Choose the queue for them to be together in - in 2 ways.
Choose Sean's position in that queue in 4 ways.
Choose Liam's position in that queue in 3 ways.
Place the remaining 6 people in the remaining 6 positions
in 6!=720 ways:

Answer: 2∙4∙3∙720=17280 

Edwin