In how many ways can the letters of the word 'LEADER' be arranged?

Concept: When the letters of a word are arranged in a row and some letters repeat, counting all letters as if they were distinct (n!) over-counts the arrangements, because swapping two identical letters with each other produces the exact same arrangement. The correct count of distinct arrangements is the factorial of the total letter count divided by the factorial of how many times each repeated letter occurs.

1. LEADER has 6 letters: L, E, A, D, E, R.

2. The letter E occurs twice; every other letter (L, A, D, R) occurs exactly once.

3. Treating all 6 letters as distinct gives 6! = 720 total orderings.

4. Because the two E's are identical, each distinct arrangement has been counted 2! = 2 times (once for each way of assigning the two E's to their positions), so we divide by 2!.

5. 720 ÷ 2 = 360 distinct arrangements.

Cross-check: this matches choosing 2 of the 6 positions for the identical E's and filling the remaining 4 positions with the 4 distinct letters (L, A, D, R) in any order — 6C2 × 4! = 15 × 24 = 360, confirming the count is internally consistent.

So the number of distinct arrangements of the letters of LEADER is 360.