In how many ways can three men and three women sit at a round table so that no two men can occupy adjacent positions?

Explanation

Since no 2 men are to sit together, there are 4 places available for them corresponding to any one way of sitting of 2 men i.e., two places between the women and 2 places are at two ends.

Let`m_1` be fixed. `m_2` can sit in 2 places, `w_1`can sit in 3 places, `m_3` can sit in 1 place. `w_2` can sit in 2 place `w_3` can sit in 1 place.`:.` The total number of ways `=2xx3xx1xx2xx1=12`