Question
Download Solution PDFIn how many ways can we sort the letters of the word MANAGEMENT so that the comparative position of vowels and consonants remains the same as in MANAGEMENT.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Word = MANAGEMENT
Calculation:
Vowel occupy 4 places then !4
∵ A and E are repeated then !4/(!2 × !2)
Consonant occupy 6 places then !6
⇒ M and N are repeated then !6/(!2 × !2)
∴ \(\frac{{!4}}{{!2\; × \;!2}}\; × \;\frac{{!6}}{{!2\; × \;!2}} = \;\frac{{4\; × 3\; × 2\; × 1}}{{2\; × 1\; × 2\; × 1}}\; × \frac{{6\; × 5\; × 4\; × 3\; × 2\; × 1}}{{2\; × 1\; × 2\; × 1}}\)
= 6 × 180 = 1080
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