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

Introduction / Context:
When letters repeat, divide the total permutations by factorials of the multiplicities. “ARMOUR” has 6 letters with R repeated twice.

Given Data / Assumptions:

• Total letters = 6; multiplicities: R × 2; A,M,O,U each × 1.

Concept / Approach:
Use 6! / 2! for the two indistinguishable R’s.

Step-by-Step Solution:

Verification / Alternative check:
Any attempt to treat both R’s as distinct would double-count each arrangement.

Why Other Options Are Wrong:
720 ignores repeated R; 540 and 300 do not correspond to the correct division.

Common Pitfalls:
Forgetting to divide by 2! for the duplicated letter.

Final Answer:
360