SOLUTION: The seats at a round table are numbered from 1 to 7. Find the number of ways in which a commitee consisting of four men and three women can be seated at the table. (a) if there ar

Question 1105438: The seats at a round table are numbered from 1 to 7. Find the number of ways in which a commitee consisting of four men and three women can be seated at the table.
(a) if there are no restrictions
(b) if all men sit together
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a) 7! = 5040, since all the chairs are numbered
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Note if the chairs are not numbered, then the answer is (7-1)! = 720
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b) the 4 men in one group can be arranged in 4! = 24 ways
the one group of 4 men and the 3 women can be arranged in 3+1 = 4! = 24 ways
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Note it is 3+1 because the chairs are numbered
:
therefore,
if all 4 men sit together, there are 4! * 4! = 24^2 = 576 ways
:

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