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Permutations of prime ministers

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  • #1
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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:
 

Answers and Replies

  • #2
96
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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.
 
  • #3
23
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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?
 
  • #4
28
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1) 7 ! / 2 !

2) 7 ! / 3!

3 ) 6 ! / 2 !
 

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