Permutations

Step 1: The word is LETTER. Letters in alphabetical order: E, E, L, R, T, T
Step 2: Count total number of permutations:


Step 3: Find the rank of TETLER:
We fix letters one by one and count how many permutations come before "TETLER".
[--] Fix first letter < T: E, L, R → try each:
E: Remaining = E, L, R, T, T →
L: Remaining = E, E, R, T, T →
R: Remaining = E, E, L, T, T →
Total before T =
[--] Fix T as 1st letter.
Now check 2nd letter < E: only E comes next, so we proceed.
[--] Fix 2nd letter = E. Remaining: E, L, R, T
[--] Fix 3rd letter < T: E, L, R
E: Remaining = L, R, T →
L: Remaining = E, R, T →
R: Remaining = E, L, T →
Total before TET... =
[--] Fix 3rd = T. Remaining: E, L, R
[--] Fix 4th < L: E → Remaining = L, R →
[--] Fix 4th = L. Remaining = E, R
[--] Fix 5th < E: none
[--] Fix 5th = E. Remaining = R
[--] 6th = R
Only this matches TETLER

Total positive integers : from 1 to 9999 = 9999 numbers Find number that do NOT contain digit 5.
We subtract that from 9999. Digits allowed (excluding 5): 0,1,2,3,4,6,7,8,9 → 9 digits Count numbers that do not have digit 5: 1-digit: 8 (1–9 except 5) 2-digit: 8 × 9 = 72 3-digit: 8 × 9 × 9 = 648 4-digit: 8 × 9 × 9 × 9 = 5832 Total = 8 + 72 + 648 + 5832 = 6560
So numbers with digit 5 at least once = 9999 - 6560 = 3439

Letters: C, U, R, V, E (5 distinct letters) Total words with at least 2 letters: Favorable: 3-letter words: