The number of 4 -letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is ____ .
Answer: 1422
Solutions · 1
Official solution
The letters available are P (\times 3), Q (\times 2), R (\times 2), S, T, U, V (\times 1 each) --- 7 distinct letters.
Case 1: All 4 letters distinct. Choose and arrange 4 of the 7 distinct letters: 7P4=7⋅6⋅5⋅4=840
Case 2: One letter repeated twice (must be P, Q, or R), other two distinct from remaining 6 letters: 3×(26)×2!4!=3×15×12=540
Case 3: Two letters each repeated twice (choose 2 from P, Q, R): (23)×2!2!4!=3×6=18
Case 4: One letter repeated three times (must be P), other one distinct from remaining 6 letters: (16)×3!4!=6×4=24
Total =840+540+18+24=1422