A school bus has 25 seats, with 5 rows of 5 seats. 15 students from the first grade and 5 students from the second grade travel in the bus. How many ways can the students be seated if all of the second-grade students occupy the first row? A. 25P20 B. 5P5 * 20P15 C. 5C5 * 25C14 D. 5P5 * 15P15 E. 5P5 * 25C15

Option B. 5P5 * 20P15

Step-by-step explanation:

It is very important to remember that the second grade students are sitting in the front row, therefore, it is only necessary to organize 15 first grade students in 20 seats.

Permutations allow you to calculate the number of ways in which m objects can be arranged in n positions.

The permutation of m in n is written as:

nPm

Where n is the number of elements and m are chosen.

The way in which the 5 second grade students can be organized in the 5 seats is from the first row is:

5P5

Then, the number of ways in which 15 first-year students can be organized into 20 seats is:

20P15

Then, the number of ways to organize all students on the bus is the product of both permutations

5P5 * 20P15