Arranging the letters of BANANA — Aptitude Question
Arranging the letters of BANANA: How many distinct arrangements are there of the letters of BANANA? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 45 seconds
Question
How many distinct arrangements are there of the letters of BANANA?
Options
- 40
- 60
- 120
- 360
Show the answer and the worked solution
Correct answer: B. 60
Worked solution
- 6 letters with A repeated 3 times and N repeated 2 times.
- Arrangements = 6!/(3! 2!) = 720/12 = 60.
Answer: 60.
The idea
Arrangements of n objects with repeats = n! divided by the product of the factorials of the repeat counts.
Shortcut. Choose places: the three A's take C(6,3) = 20 sets of slots, the two N's C(3,2) = 3 of the rest, and B the last — 20 × 3 = 60.
Common trap. 120 — dividing 6! by 3! for the A's but forgetting the two N's; 720 ÷ 6 must be halved again.
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