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 of the second-grade students occupy the first row?

a. 25P20
b. 5P5 × 20P15
c. 5C5 × 25C14
d. 5P5 × 15P15
e. 5P5 × 25C15

Answer 1

b

Explanation:

plato fam

Answer 2

The correct option is b.

Explanation:

It is given that the school bus has 25 seats, with 5 rows of 5 seats.

The number of students from the first grade is 15 and the number students from the second grade is 5.

The formula to arrange r items in n places is

`^nP_r=(n!)/((n-r)!)`

The number of seats in first row is 5 and the number students from the second grade is 5. So, the total number of arrangement is

`^5P_5`

The number of seats except first row is 20 and the number students from the first grade is 15. So, the total number of arrangement is

`^(20)P_(15)`

The total number of ways the students can be seated if all of the second-grade students occupy the first row is

`^5P_5* ^(20)P_(15)`

Therefore the correct option is b.