Multiple choice

A group of 10 students is to be lined up in a straight line. In how many different ways can the students be arranged if two particular students must not stand next to each other?

  1. 2,303,440

  2. 2,309,040

  3. 2,903,040

  4. 3,903,040

  5. 3,902,440
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total arrangements of 10 students is 10!. Arrangements where two specific students are together is 9! * 2!. Subtracting this from total: 10! - 2 * 9! = 9!(10 - 2) = 8 * 9! = 8 * 362,880 = 2,903,040.

AI explanation

The total arrangements for 10 students is 10! = 3628800. Treating the two particular students as one unit gives 9! * 2! = 725760 arrangements where they stand together. Subtracting the adjacent arrangements gives 3628800 - 725760 = 2903040 ways.

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