Final answer:
To find the probability that there will be exactly 3 men between A and B, we need to consider the total number of possible arrangements and the number of favorable arrangements that satisfy the given condition. The probability is 1/3.
Step-by-step explanation:
To find the probability that there will be exactly 3 men between A and B, we need to consider the total number of possible arrangements and the number of favorable arrangements that satisfy the given condition.
The total number of arrangements can be calculated as 10!, which is the number of ways to arrange 10 men in a row.
The number of favorable arrangements can be calculated as 8! * 2, because there are 8 men remaining after A and B are placed, and we need to account for the possible arrangements of those 8 men as well as the two arrangements of A and B.
Therefore, the probability is (8! * 2) / 10!, which simplifies to 1/3.