Multiple choice

Directions: Answer the questions independently of each other. How many different words (not necessarily meaningful) can be formed if all the letters of the word 'RAVINA' are to be arranged such that 'I' is always somewhere between the 2 A's?

  1. 24

  2. 120

  3. 64

  4. 60
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total letters = 6 (R, A, V, I, N, A). Total arrangements = 6! / 2! = 360. The condition 'I is between the two A's' means in any arrangement of the 3 letters (A, I, A), there is only 1 valid order (A, I, A). Since there are 3 positions for these 3 letters out of 6, we divide the total arrangements by 3 (the number of ways to arrange A, I, A). 360 / 3 = 120.

AI explanation

The word RAVINA contains 6 letters where 2 are A's and the remaining 4 (R, V, I, N) are distinct, giving 6! / 2! = 360 total arrangements. Because the two A's are identical, out of the 3 relevant items (A, I, and A), the letter I is equally likely to be in any of the 3 possible relative positions. There is exactly 1 position where I sits between the two A's, so we take 1/3 of the total arrangements. Calculating 360 / 3 gives 120 arrangements.

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