Four men and three women are to be seated at a lunch counter that has only five stools. In how many ways can these people be arranged at the counter?

To arrange four men and three women at a lunch counter with five stools, we first choose any five individuals from the total of seven (four men and three women). The number of ways to choose five people from seven is given by the combination formula ( \binom{7}{5} = 21 ). After selecting the five individuals, they can be arranged in ( 5! = 120 ) different ways. Therefore, the total number of arrangements is ( 21 \times 120 = 2520 ).