Multiple choice

In how many ways can 10 persons (A to J) stand in 2 rows with 5 persons per row, such that A should always be in the second row and C should always be in the first row?

  1. 25 × 8!

  2. 5P2 × 5P2

  3. 4P2 × 4P2

  4. 4! × 4!

  5. 8!
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A Correct answer
Explanation

There are 10 positions (5 in each row). A must be in row 2 (5 choices), C must be in row 1 (5 choices). The remaining 8 people can be arranged in the remaining 8 spots in 8! ways. Total ways = 5 * 5 * 8! = 25 * 8!.

AI explanation

Place person C in any of the 5 spots in the first row and person A in any of the 5 spots in the second row, yielding 5 times 5 ways. The remaining 8 people can then be arranged in the remaining 8 positions in 8! ways. The total number of ways is 25 times 8!.

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