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 the first-grade students occupy the first 3 rows?

\\(_{25}p_{20}\\)

\\(_{5}p_{5} \times {}_{20}p_{15}\\)

\\(_{15}c_{15} \times {}_{10}c_{5}\\)

\\(_{15}p_{15} \times {}_{10}p_{5}\\)

\\(_{15}p_{15} \times {}_{10}c_{5}\\)

Explanation:

Seat the first-grade students in the first 3 rows

$$ {}_{15}\text{P}_{15} $$

Seat the second-grade students in the remaining seats

$$ {}_{10}\text{P}_{5} $$

Combine the independent seating arrangements

$$ {}_{15}\text{P}_{15} \times {}_{10}\text{P}_{5} $$

Answer:

• (A) \({}_{25}\text{P}_{20}\)
• (B) \({}_{5}\text{P}_{5} \times {}_{20}\text{P}_{15}\)
• (C) \({}_{15}\text{C}_{15} \times {}_{10}\text{C}_{5}\)
• (D) \({}_{15}\text{P}_{15} \times {}_{10}\text{P}_{5}\) (Correct answer)
• (E) \({}_{15}\text{P}_{15} \times {}_{10}\text{C}_{5}\)