Multiple choice

Two out of six papers for an examination are to be on Mathematics. In how many ways can the papers be arranged so that the two Mathematics papers do not fall together?

  1. 240

  2. 480

  3. 720

  4. 800

  5. 915
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total arrangements of 6 papers = 6! = 720. Treat the 2 Math papers as one unit. Arrangements with Math together = 5! * 2! = 120 * 2 = 240. Arrangements with Math not together = 720 - 240 = 480.

AI explanation

The total number of ways to arrange all 6 papers without restriction is 6 factorial, which equals 720. If the two Mathematics papers are treated as a single unit, they can be arranged with the other 4 papers in 5 factorial ways, and the two Mathematics papers can switch places within their unit in 2 factorial ways, yielding 120 multiplied by 2, or 240 arrangements. Subtracting the arrangements where the math papers are together from the total unrestricted arrangements gives 720 minus 240, which is 480.

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