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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The number of $4$-letter words, with or without meaning, which can be formed using the letters $PQRPRSTUVP$, is ______.
Solution
$P \to 3,; Q \to 2,; R \to 2,; S,T,U,V \to 1$
Case I: 3 alike, 1 different
${}^1C_1 \times {}^6C_1 \times \dfrac{4!}{3!} = 24$
Case II: 2 alike, 2 alike
${}^3C_2 \times \dfrac{4!}{2!2!} = 18$
Case III: 2 alike, 2 different
${}^3C_1 \times {}^6C_2 \times \dfrac{4!}{2!} = 540$
Case IV: All 4 different
${}^7C_4 \times 4! = 840$
Total words $= 1422$
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