Question

In how many ways may 6 Hindus and 6 Muslims sit around a round table so that two Hindus may never sit together?

Answer 1

Fix up a Muslim and the remaining 5 Muslims can be seated in 5! ways. Now no two Hindus are to sit together and as such the 6 Hindus are to be arranged in six empty seats between two consecutive Muslims and number of arrangements will be 6!.
Hence by fundamental theorem the total number Of ways is 5! x6! = 120 x 720 = 86400.