In how many ways can six men be arranged in a straight row so that the oldest of them is at the beginning of the row?

To arrange the six men in a straight line such that the oldest man is at the beginning of the line, we can follow these steps:

1. Choose the oldest man and place him at the beginning of the line. There is only 1 way to do this.

2. Arrange the remaining 5 men in any order behind the oldest man. There are 5! = 120 ways to arrange the rest of the men.

3. Multiply the number of ways from step 1 and step 2 to get the total number of ways to arrange the six men.

Therefore, the total number of ways to arrange the six men in a straight line with the oldest man at the beginning is: 1 \times 5! = 1 \times 120 = \boxed{120}.

\boxed{120}