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Question

A person writes letters to 6 friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least 4 of them are in wrong envelopes ?

  1. 72  
  2. 719  
  3. 664  
  4. 135  

The correct answer is: 664


    No. of ways = 6C2 . 4!open parentheses 1 – fraction numerator 1 over denominator 1 factorial end fraction plus....... plus fraction numerator 1 over denominator 4 factorial end fraction close parentheses + 6C15! open parentheses 1 – fraction numerator 1 over denominator 1 factorial end fraction plus....... – fraction numerator 1 over denominator 5 factorial end fraction close parentheses+ 6C0 . 6! open parentheses 1 – fraction numerator 1 over denominator 1 factorial end fraction plus....... plus fraction numerator 1 over denominator 6 factorial end fraction close parentheses
    = 135 + 264 + 265 = 664

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