How many distinguishable permutations of the letters in the word BANANA are…
2017
How many distinguishable permutations of the letters in the word BANANA are there ?
- A.
720
- B.
120
- C.
60
- D.
360
Attempted by 128 students.
Show answer & explanation
Correct answer: C
Answer: 60
Explanation: Count permutations of the six letters in BANANA while correcting for identical letters.
Total letters: 6. Multiplicities: A appears 3 times, N appears 2 times, B appears 1 time.
Use the formula for permutations with repeated items: number = 6! / (3! · 2! · 1!).
Compute factorials: 6! = 720, 3! = 6, 2! = 2. So number = 720 / (6 × 2) = 720 / 12 = 60.
Note: A common error is to treat letters as all distinct (giving 720) or to account for only one set of repeats (giving 120 or 360). Always divide by the factorial of each repeated count.