jakolik wrote:
Seven men and five women have to sit around a circular table so that no 2 women are together. In how many different ways can this be done?
Quote:
the qs only says that the Women should not sit next 2 each other... but men can right? so y are we assuming
M_M_M_M_M_M_M_ : 14 Places
we can also have:
M_M_M_M_M_MMM: 12 places
MMM_M_M_M_M_M: 12 places
in this case the answer will be:
6!*5! right??
Also, i am not understanding how Bunnel got 21!
Yes, men can sit together but women cannot.
Don't assume places to be empty chairs. Think of a big round table. Each person who comes and sits around the table, brings his/her own chair along. Say the 7 men come and sit around the round table. They will be able to do that in 6! ways. Now, there is space between each pair of men. How many distinct spaces are there? 7 because there are 7 men say M1, M2, M3 till M7. So now you have empty space to the right of M1 and right of M2 and right of M3 etc. The women can take any 5 of these 7 spaces. Note that 2 women cannot take the same space because two women cannot sit together.
Say, the 5 women took 5 spots each to the right of M1, M2, M3, M4 and M5. So now spaces to the right of M6 and M7 are vacant. This means M6, M7 and M1 are sitting together with no one in between them. This takes care of the cases you have pointed out. So when we select 5 of the 7 spaces, we take care of all cases.
In how many ways can 7 men sit around a circular table? In 6! ways.
In how many ways that women select 5 of the 7 distinct places and arrange themselves in those places? In 7C5 * 5! ways.
Total arrangements = 6!* 7C5 * 5!
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Karishma
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