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?

a.) 25P20

b.) 5P5 × 20P15
c.) 15C15 × 10C5
d.) 15P15 × 10P5
e.) 15P15 × 10C5

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flightbath flightbath · Answer 1 · 2018-11-21T09:48:28+01:00

Answer:

Option D is correct that is 15P15 x 10P5

Explanation:

There are total 15 students in first grade and total 5 rows of 5 seats

so, students of first grade can be arranged to occupy the seats in 15P15

And there are total 5 students in second grade

Since, 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 2 is 10P5

Hence, The correct Option is D 15P15 x 10P5

joaobezerra joaobezerra · Answer 2 · 2022-02-14T14:08:03+01:00

Using the combination formula, it is found that the number of ways in which the students can be seated is given by:

c.) 15C15 × 10C5

The order in which the students are seated is not important, hence the combination formula is used.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem:

The 15 seats in the first 3 rows is for the 15 first grade students, hence [tex]C_{15,15}[/tex].

The 10 seats on the last 2 rows is for the 5 second grade students, hence [tex]C_{10,5}[/tex].

The total number is:

[tex]T = C_{15,15} \times C_{10,5}[/tex].

Hence option C is correct.

You can learn more about the combination formula at https://brainly.com/question/25821700