Multiple choice

A TCYonline test contains 15 different questions with one question being the easiest and one being the toughest. In how many ways can these questions be arranged, one after the other, so that the easiest and the toughest question never appear together?

  1. 14! – 2!

  2. 15! – 2!

  3. 15! – (2!13!)

  4. 15! – (2!14!)

  5. 14!
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total arrangements of 15 questions is 15!. Arrangements where the two specific questions are together: treat them as one unit, so 14! * 2!. Thus, arrangements where they are NOT together = 15! - (2! * 14!).

AI explanation

The total number of ways to arrange the 15 different questions is 15 factorial. If we treat the easiest and toughest questions as a single block, this block can be arranged with the remaining 13 questions in 14 factorial ways, and the two questions can be arranged within the block in 2 factorial ways. The number of ways they appear together is therefore 2 factorial times 14 factorial. We subtract this from the total arrangements to get 15 factorial minus (2 factorial times 14 factorial).

Keep practicing — related questions