Question: The number of ways in which 5 male and 2 female members of a committee can be seated around a round ...

Question

The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two female are not seated together is

Answer 1

Solution

Fix up a male and the remaining 4 male can be seated in 4! ways. Now no two female are to sit together and as such the 2 female are to be arranged in five empty seats between two consecutive male and number of arrangement will be $5P_{2}$ . Hence by fundamental theorem the total number of ways is = $4! \times^{5} ⥂ P_{2} = 24 \times 20 = 480$ ways.