Question
The number of 4 -letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is \_\_\_\_.
JEE Main
Mathematics
Permutation Combination
2026
JEE Main 2026 (23 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
Letters: P(3), Q(2), R(2), S(1), T(1), U(1), V(1) — 7 distinct letters. All distinct: 7 4 4! = 840. One pair + 2 distinct: choose repeating letter from \ P,Q,R\ (3 ways), choose 2 from remaining 6 ( 6 2 =15), arrange = 4!/2! = 12. Total = 3 15 12 = 540. Two pairs: choose 2 from \ P,Q,R\ ( 3 2 =3), arrange = 4!/(2!2!) = 6. Total = 18. One triple + 1 distinct: only P can repeat 3 times, choose 1 from 6, arrange = 4!/3! = 4. Total = 24. Answer = 840 + 540 + 18 + 24 = 1422.
Related: Mathematics — Permutation Combination · All PYQ Banks