Permutations of prime ministers

[fork]

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.

Thanks :rofl:

 

[Emieno]

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.

 

[fork]

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?

 

[Mithal]

1) 7 ! / 2 !

2) 7 ! / 3!

3 ) 6 ! / 2 !