Permutations of BANANA: How many distinct permutations of the letters in BANANA are possible?

Introduction / Context:BANANA contains repeated letters, so we count distinct permutations by dividing total factorial by repeated-letter factorials.

Given Data / Assumptions:Letters: A×3, N×2, B×1; total letters = 6.

Concept / Approach:Distinct permutations = 6! / (3! * 2!).

Step-by-Step Solution:

Verification / Alternative check:Sanity check with smaller multisets (e.g., AAB) supports the approach.

Why Other Options Are Wrong:270, 120, 360 are not equal to 6!/(3!*2!).

Common Pitfalls:Missing one of the repeated-letter divisors.

Final Answer:60