Question

Select the correct answer.
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?
OA 25P20
OB. SPs * 20P15
OC5C525C14
OD. SPs *15P15
OE PSX25C5

Answer 1

Answer:

B. $^{5} P_{5}$ × $^{20} P_{15}$

Step-by-step explanation:

No. of students from first grade = 15

No. of students from second grade = 5

There are 5 rows of seats

Each row contains 5 seats

Total seats = 25

No. of ways for second-grade students to occupy the first row (i.e first 5 seats) = $^{5} P_{5}$

Remaining seats = 20

So, now we are left with 15 first grade students  

So, No. of ways for first-grade students occupy remaining seats = $^{20} P_{15}$

Using the counting rule principle,

No. of ways for the students can be seated if all of the second-grade students occupy the first row = $^{5} P_{5}$ × $^{20} P_{15}$

So, Option B is the correct answer

Hence, no. of ways for the students can be seated if all of the second-grade students occupy the first row is ×