Answered

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?

A25P20
B5P5 × 20P15
C5C5 × 25C14
D5P5 × 15P15
E5P5 × 25C15

Verified Answer :

Answer:

The correct option is b.

Step-by-step 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

\(^nP_r=\frac{n!}{(n-r)!}\)

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

\(^5P_5\times ^{20}P_{15}\)

Therefore the correct option is b.

teebstays

Answer:

b

Step-by-step explanation:

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