The number of ways in which 100 persons may be seated at 2 round tables T1 and T2 , 50 persons being seated at each is
Question
The number of ways in which 100 persons may be seated at 2 round tables T1 and T2 , 50 persons being seated at each is
Solution
The problem can be solved using the concept of permutations and combinations.
Step 1: Select 50 people to sit at table T1. This can be done in C(100, 50) ways.
Step 2: Arrange these 50 people around table T1. Since it is a round table, the number of arrangements is (50-1)!, because in a circular permutation, the number of ways to arrange n items is (n-1)!.
Step 3: The remaining 50 people will sit at table T2. Arrange these 50 people around table T2. The number of arrangements is also (50-1)!.
Step 4: Multiply the number of ways from each step together to get the total number of ways.
So, the total number of ways is C(100, 50) * (50-1)! * (50-1)!.
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