CA Foundation · Quantitative Aptitude · Permutations and Combinations
How many distinct arrangements can be made using all the letters of the word 'BANANA' in which the letters are placed in a row?
There are 60 distinct arrangements. The word has six letters, with A appearing three times and N twice. Dividing the total permutations by the repeats gives 6!/(3!×2!) = 720/12 = 60. Ignoring one of the repetitions would give a wrong larger number.
- A720
- B120
- C60Correct
- D30
Explanation
BANANA has 6 letters with A repeated 3 times and N repeated 2 times. Arrangements = 6!/(3!×2!) = 720/12 = 60. Option 120 divides only by 3!, ignoring the repeated N.
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