In 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.

This question was previously asked in
UP Police SI (दरोगा) Previous Paper 2 (Held On: 13 Dec 2017 Shift 3)
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  1. 1280
  2. 720
  3. 960
  4. 1080

Answer (Detailed Solution Below)

Option 4 : 1080
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यूपी पुलिस SI (दरोगा) सामान्य हिंदी मॉक टेस्ट
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Detailed Solution

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Given:

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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