In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together: 

Fix up 1 man and the remaining 6 men can be seated in 6! ways. Now no two women are to sit together and as such the 7 women are to be arranged in seven empty seats between two consecutive men and number of arrangement will be 7!. Hence by fundamental theorem the total number of ways $=7!\times 6!$