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CA Foundation · Quantitative Aptitude · Permutations and Combinations

In how many distinct ways can the letters of the word 'BALLOON' be arranged so that the two L's are not adjacent?

The answer is 900. Total arrangements of BALLOON are 7!/(2!·2!) = 1260. With the two L's glued together there are 6!/2! = 360 arrangements. Subtracting gives 1260 − 360 = 900 arrangements where the L's are apart.

  1. A1260
  2. B900Correct
  3. C1800
  4. D630

Explanation

BALLOON has 7 letters with L twice and O twice. Total = 7!/(2!·2!) = 1260. L's together: treat LL as one unit, giving 6 units with O twice: 6!/2! = 360. Not together = 1260 − 360 = 900. The value 630 comes from wrongly dividing by 2 again.

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