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Permutations of prime ministers

  1. Sep 24, 2005 #1
    The prime ministers A, B, C, D, E, F and G of 7 countries will address at a summer meeting.
    a) Find the number of arrangerments that can be made so that
    1)A will speak before C,
    2)A will speak before C and C will speak before E.
    b)In how many of those ways in a2) will C speak immediately after A?

    I stump in this question. :confused:

    Thanks :rofl:
     
  2. jcsd
  3. Sep 25, 2005 #2
    a.1) A: 1st~6th position, C takes a 2th~7th one, count the two numbers, then just do a multiplication on both (A gets the first one, C runs from 2~7, A get the second one, C runs from 3 to 7...etc )
    a.2) A: 1st~5th, C is in 2~6, E is in 3~7, then do the same as a.1's(...)
    b)Because there are only 7 groups, counting is a natural, easy way to reasoning a solution, this b question still can be done in the same fashion.
     
  4. Sep 25, 2005 #3
    The answer from a1 to b are 2520, 840 and 360 respectively.

    I don't know how to obtain the result from the above counting.

    Thanks for your answering.

    Also, are there any quicker methods of doing this question?
     
  5. Sep 28, 2005 #4
    1) 7 ! / 2 !

    2) 7 ! / 3!

    3 ) 6 ! / 2 !
     
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