Answer:

To find the total number of sitting arrangements of 7 persons in a row if 2 persons occupy the end seats, we can consider these two persons as a single entity. So essentially, we have 6 entities (5 single persons and 1 pair of persons) to arrange in a row.

Step 1: Find the total number of arrangements of 6 entities in a row.

The number of arrangements of n entities in a row is given by n!.

Therefore, the total number of arrangements of 6 entities in a row is 6!.

Step 2: Consider the pair of persons as a single entity and find the number of arrangements of this single entity and the remaining 4 single persons.

Since we have a single entity (pair of persons) and 4 other single persons, the number of arrangements of these 5 entities in a row is 5!.

Step 3: Multiply the results from Step 1 and Step 2 to get the total number of arrangements.

The total number of arrangements is given by (6!) * (5!).

Therefore, the correct answer is option C: 2! * 5!.

Explanation:

When 2 persons occupy the end seats, they can be treated as a single entity. Now we have a total of 6 entities (5 single persons and 1 pair of persons) to arrange in a row.

To find the total number of arrangements, we need to consider the arrangements of these 6 entities. The number of arrangements of n entities in a row is given by n!.

However, since the pair of persons is treated as a single entity, we need to consider the arrangements of this single entity and the remaining 4 single persons. The number of arrangements of these 5 entities in a row is given by 5!.

Therefore, the total number of arrangements is obtained by multiplying the results from Step 1 and Step 2, which gives us (6!) * (5!).

Hence, the correct answer is option C: 2! * 5!.