Assume that three men and three women are to sit in a row of six chairs. In how many ways can these people sit if all men must sit together and all the women must sit together? Use the fundamental counting principle. To apply this principle, first identify the separate tasks involved in making the seating arrangements.

Step 1 ：First, consider the group of men as a single entity and the group of women as another single entity. So, we have two entities to arrange in two places, which can be done in \(2!\) ways.

Step 2 ：Next, arrange the three men among themselves and the three women among themselves. Each of these can be done in \(3!\) ways.

Step 3 ：According to the fundamental counting principle, the total number of ways these people can sit is the product of the number of ways to perform each of these tasks.

Step 4 ：So, the total number of ways is \(2! * 3! * 3!\) = \(2 * 6 * 6\) = \(72\).

Step 5 ：Final Answer: The total number of ways these people can sit if all men must sit together and all women must sit together is \(\boxed{72}\).