Multiple choice

In how many ways can 13 different alphabets (a, b, c.......m) be arranged so that the alphabets f and g never come together?

  1. 13! - 12!

  2. 13! - 12!/2!

  3. 13! - 2 x 12!

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total arrangements of 13 letters is 13!. Treating 'fg' as a single block, there are 12! ways to arrange the items, and 2! ways to arrange f and g within the block. Thus, the number of ways they are together is 2 * 12!. Subtracting this from total gives 13! - 2 * 12!.

AI explanation

The total number of ways to arrange 13 different alphabets is 13!. To find the arrangements where f and g are together, we treat them as a single unit, which can be internally arranged in 2! ways. This combined unit leaves us with 12 units to arrange, giving 2 * 12! arrangements where they are together. Subtracting the cases where they are together from the total gives the number of arrangements where they never come together as 13! - 2 * 12!.

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