Final answer:
To answer the question regarding the number of ways 3 boys and 4 girls can sit in a row, we calculate 7 factorial (7!), which equates to 5040 different arrangements, as each of the 7 individuals can occupy a distinct position in the ordering.
Step-by-step explanation:
The question posed is one of permutation and combination, a common topic in mathematics. Specifically, it asks us to calculate the number of ways in which 3 boys and 4 girls can sit in a row. This is a straightforward permutation problem since the order in which they sit matters.
To solve this, we consider that each person (boy or girl) is a distinct individual. We have a total of 7 people (3 boys + 4 girls), and we want to find out how many different ways we can arrange these 7 people in a row. The solution involves computing a factorial, which is denoted by '!' and is a product of all positive integers up to a given number.
The number of ways 7 people can sit in a row is calculated by using 7 factorial (7!). The factorial of 7 (written as 7!) is the product of all positive integers from 1 to 7, which is 7 x 6 x 5 x 4 x 3 x 2 x 1. Therefore, the answer to our problem is 7! = 5040 distinct arrangements. This number represents all the different ways the 3 boys and 4 girls can be seated in a row.