Multiple choice

In how many different ways can be the letters of the word 'KABRISTAN' be arranged so that all vowel come together ?

  1. 15220

  2. 15120

  3. 15140

  4. 15620

  5. 2160
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

KABRISTAN has 9 letters with vowels A, I, A (3 vowels). Treat the 3 vowels as one unit. We have 7 items to arrange (K,B,R,S,T,N and the vowel unit). These can be arranged in 7! ways. The 3 vowels within their unit can be arranged in 3!/2! ways (since A repeats twice). Total = 7! × (3!/2!) = 5040 × 3 = 15120. Option B is correct. This uses the permutation formula for arranging items with some items grouped together.

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