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?

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

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

\\(_{5}c_{5} \times _{25}c_{14}\\)

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

\\(_{5}p_{5} \times _{25}c_{15}\\)

Explanation:

Calculate seating arrangements for second-grade students

$$ {}_{5}P_{5} $$

Calculate seating arrangements for first-grade students

$$ {}_{20}P_{15} $$

Find the total number of ways

$$ {}_{5}P_{5} \times {}_{20}P_{15} $$

Answer:

• (A) \({}_{25}P_{20}\)
• (B) \({}_{5}P_{5} \times {}_{20}P_{15}\) (Correct answer)
• (C) \({}_{5}C_{5} \times {}_{25}C_{14}\)
• (D) \({}_{5}P_{5} \times {}_{15}P_{15}\)
• (E) \({}_{5}P_{5} \times {}_{25}C_{15}\)