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JEE Main 202623 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
23 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2026 · 23 January · Morning Shift · Mathematics · Permutation and Combination

The number of 4 -letter words, with or without meaning, which can...

The number of 4 -letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is ____\_\_\_\_.

Correct answer

1422

Step-by-step solution

Letters: P(3), Q(2), R(2), S(1), T(1), U(1), V(1) — 7 distinct letters.
All distinct: (74)×4!=840\binom{7}{4} \times 4! = 840.
One pair + 2 distinct: choose repeating letter from {P,Q,R}\{P,Q,R\} (3 ways), choose 2 from remaining 6 ((62)=15\binom{6}{2}=15), arrange =4!/2!=12= 4!/2! = 12. Total =3×15×12=540= 3 \times 15 \times 12 = 540.
Two pairs: choose 2 from {P,Q,R}\{P,Q,R\} ((32)=3\binom{3}{2}=3), arrange =4!/(2!2!)=6= 4!/(2!2!) = 6. Total =18= 18.
One triple + 1 distinct: only P can repeat 3 times, choose 1 from 6, arrange =4!/3!=4= 4!/3! = 4. Total =24= 24.
Answer =840+540+18+24=1422= 840 + 540 + 18 + 24 = 1422.
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