Multiple choice

If the letter of the word $ASHOKA$ are written down at randomly, then the chance that all A's are consecutive is

  1. $\cfrac { 1 }{ 3 } $
  2. $\cfrac { 1 }{ 4 } $
  3. $\cfrac { 2 }{ 3 } $
  4. $\cfrac { 1 }{ 2 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total arrangements of ASHOKA = 6! / 2! = 360. Treating the two A's as a single unit, we have 5 units (AA, S, H, O, K), which can be arranged in 5! = 120 ways. Probability = 120 / 360 = 1/3.

AI explanation

Treat the two A's as a single combined letter, which means you are arranging 5 units total. The total number of arrangements of the 6 letters is 6 factorial divided by 2 factorial, which is 360. The number of favorable arrangements where the A's are together is 5 factorial, which is 120, so the probability is 120 divided by 360, resulting in 1 over 3.

Keep practicing — related questions