Mathematics · Permutations and Combinations

JEE Main 2026 — 23 January, Morning Shift — Question 25

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

Answer: 1422

Numerical answer — enter this value.

$\mathrm{P} \rightarrow 3, \mathrm{Q} \rightarrow 2, \mathrm{R} \rightarrow 2, \mathrm{~S}, \mathrm{~T}, \mathrm{U}, \mathrm{V}$

Case I 3 alike, 1 different ${ }^{1} \mathrm{C}_{1} \times{ }^{6} \mathrm{C}_{1} \times \frac{4!}{3!}=24$

Case II 2 alike, 2 alike ${ }^{3} \mathrm{C}_{2} \times \frac{4!}{2!2!}=18$

Case III 2 alike, 2 different ${ }^{3} \mathrm{C}_{1} \times{ }^{6} \mathrm{C}_{2} \times \frac{4!}{2!}=540$

Case IV All 4 different ${ }^{7} \mathrm{C}_{4} \times 4!=840$

Total words $=1422$

Answer key and solution verified before publishing.

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