Given three integers N, X and Y. The task is to find the number of ways to arrange 2*N persons along two sides of a table with N number of chairs on each side such that X persons are on one side and Y persons are on the opposite side.
Note: Both X and Y are less than or equals to N.
Input : N = 5, X = 4, Y = 2
Output : 57600
The total number of person 10. X men on one side and Y on other side, then 10 – 4 – 2 = 4 persons are left. We can choose 5 – 4 = 1 of them on one side in ways and the remaining persons will automatically sit on the other side. On each side arrangement is done in 5! ways. The number of ways is .5!5!
Input : N = 3, X = 1, Y = 2
Output : 108
The total number of person 2*N. Let call both the sides as A and B. X men on side A and Y on side B, then 2*N – X – Y persons are left. We can choose N-X of them for side A in ways and the remaining persons will automatically sit on the other side B. On each side arrangement is done in N! ways. The number of ways to arrange 2*N persons along two sides of a table is .N!N!
Below is the implementation of the above approach :
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- Find the type of triangle from the given sides
- Calculate Stirling numbers which represents the number of ways to arrange r objects around n different circles
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