How many distinct arrangements can be made from the letters of “BANKING”? (N appears twice; other letters are distinct.)

Introduction / Context:To count permutations of a word with repeated letters, divide n! by factorials of multiplicities. “BANKING” has 7 letters with N repeated twice.

Given Data / Assumptions:

• Total letters = 7; multiplicity: N × 2.

Concept / Approach:Compute 7! / 2!.

Step-by-Step Solution:

Verification / Alternative check:Listing patterns confirms that exchanging the two N’s does not produce a new arrangement, hence the 2! divisor.

Why Other Options Are Wrong:5040 ignores repetition; 2540 and 5080 are not valid factorial-based counts.

Common Pitfalls:Overlooking exact multiplicities or dividing by the wrong factor.

Final Answer:2520