Round Table
Round Table
combinatorial math question, how many ways can people seated in a round table?
How many ways can Seat 5 men, 5 women and 1 dog in a round table, if men can not sit side by side, women either?
Let us assume that the dog is not a moment. Then, the seats alternating man male female woman ... Then choose an arbitrary man, puts it in the first president. Now there are 4 possibilities for man along with two chairs on the right, then 3 possibilities for man with two chairs ... leader 4! Now, the woman must be brought in the chair is everyone else. There are 5 seats possible for the first wife (or you could choose an arbitrary president and find that there are 5 women as possible for him). Using the logic above, we have 5!. Therefore, the total number of alternative forms of 5 men and 5 women around a circular table is 4! * 5!. Note that the circular table means that if everybody slides down a president is the same result that counts, it will. Finally, it is possible for each head of population, the dog can be classified between the two adjacent, leading to a factor of 10 (10 seats for example). Thus the final answer is: 4! * 5! * 10 = 2 * (5!) ² = 28,800
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