Aschool 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?

5P5×20P15

Step-by-step explanation:

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.

second-grade students occupy the first row.

The 5 students of second grade are to be seated in 5 seats,this can be done in:

5P5 ways where P is the permutation

Now 15 students from first grade are to be arranged in remaining 20 seats

This can be done in:

20P15 ways

Hence, total ways student can be seated is:

5P5×20P15

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: