Four men and three women are to be arranged at a round table. The number of arrangements in which no two women are together is ....

Step-by-step solution

First, arrange the 4 men around the circular table. The number of ways to do this is (4 - 1)! = 3! . When the 4 men are seated, they create 4 gaps between them. To ensure that no two women sit together, the 3 women must be placed in these 4 gaps. The number of ways to choose 3 gaps out of 4 and arrange the 3 women in them is ⁴P₃ = 4 3 2 = 4! . Therefore, the total number of arrangements is 3! 4! . Answer: 3! 4!