How many distinct arrangements of the letters in “FINANCE” are possible? (N appears twice; other letters are distinct.)

Introduction / Context:Again a multiset permutation: 7 letters with a duplication of N. The standard formula applies.

Given Data / Assumptions:

• Letters: F, I, N, A, N, C, E (N × 2).

Concept / Approach:7! / 2! counts distinct arrangements since interchanging the two N’s does not create a new word.

Step-by-Step Solution:

Verification / Alternative check:Check multiplicities: only N repeats; no other repeated letters.

Why Other Options Are Wrong:5040 ignores repetition; 1260 or 840 divide by too much.

Common Pitfalls:Misidentifying repeat counts in the word.

Final Answer:2520