Question

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 the first-grade students occupy the first 3 rows?

Answer 1

THe first graders sit in the first 3 row of seats, and the second graders sit in the 4th row of seats and the 5 row will be empty.

Answer 2

`^(15)P_(15)* ^(10)P_(5)`

Explanation:

Given : 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.

To find : How many ways can the students be seated if all the first-grade students occupy the first 3 rows?

Solution :

Total number of seats = 25

Number of rows and seats are = 5 rows of 5 seats

So, Number of students in first grade = 15

Number of students in second grade = 5

Now, The students of first grade can be arranged to occupy the seats in

`^(15)P_(15)`

We have total 25 seats 15 seats are already occupied

So, number of seats now available is 10

Arrangement of seats for students of grade second is
`^(10)P_(5)`

Therefore, Number of ways can the students be seated if all the first-grade students occupy the first 3 rows

`^(15)P_(15)* ^(10)P_(5)`