Multiple choice

In how many different ways the letters of the word 'SHAKESPEAR' can be arranged such that no two 'A' come together. Repetition of letters is not allowed

  1. 10!

  2. 9!

  3. 9!/2!

  4. 10!/2!
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The word SHAKESPEAR has 10 letters with two A's. To ensure no two A's are together, we arrange the 8 non-A letters in 8! ways, then place the 2 A's in the 9 available gaps (including ends) using 9P2 ways. The total is 8! * (9 * 8 / 2) * 2 = 9!.

AI explanation

The 10 letters in SHAKESPEAR can be arranged in 10!/2! ways because of the two A's. To ensure no two A's come together, we place the two A's in the 9 spaces around the 8 other distinct letters, giving 9P2 arrangements for the A's. The remaining 8 distinct letters arrange in 8! ways, yielding (9P2 * 8!) = 9! arrangements.

Keep practicing — related questions