Question 913724: I want to find all the ways to order 5 people (numbered 1:5) in 3 rows (rows a:c).
the only constraint is that each row can contain only 3 people.
What i am looking for is the formula to do this.
Any help would be appreciated
thanks
Found 2 solutions by rothauserc, josmiceli:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! You want the formula for permutations without repetition. The formula is
(nPr) = n! / (n-r)! where ! = factorial
(5P3) = (5*4*3*2*1) / (5-3)! = 20 = 20 possible permutations
Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! The rows ( a,b,c ) can be filled as follows:
1,1,3
1,3,1
3,1,1
------
1,2,2
2,1,2
2,2,1
------
These are NOT allowed:
0,1,4
1,0,4
0,4,1
1,4,0
4,0,1
4,1,0
----
5,0,0
0,5,0
0,0,5
----
Each of the ( allowed ) seating plans
can have 
so, there can be
 possible seatings
This is my best guess
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