The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is __________. [2026]

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Solution

Q.
The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is __________. [2026]

Ans.
(1422)

$P \to 3, Q \to 2, R \to 2, S, T, U, V$

$Case I: 3 alike, 1 different$

${}^{1}C_{1} \times {}^{6}C_{1} \times \frac{4!}{3!} = 24$

$Case II: 2 alike, 2 alike$

${}^{3}C_{2} \times \frac{4!}{2! 2!} = 18$

$Case III: 2 alike, 2 different$

${}^{3}C_{1} \times {}^{6}C_{2} \times \frac{4!}{2!} = 540$

$Case IV: All 4 different$

${}^{7}C_{4} \times 4! = 840$

$Total words = 1422$

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