Maths-
General
Easy

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  = blank to the power of 6 straight C subscript 2.4 factorial times open parentheses 1 minus fraction numerator 1 over denominator 1 factorial end fraction plus horizontal ellipsis plus fraction numerator 1 over denominator 4 factorial end fraction close parentheses times plus to the power of 6 straight C subscript 1.5 factorial open parentheses 1 minus fraction numerator 1 over denominator 1 factorial end fraction plus horizontal ellipsis minus fraction numerator 1 over denominator 5 factorial end fraction close parentheses times plus times to the power of 6 straight C subscript stack 0 with _ below with _ below.. end subscript times 6 factorial
    open parentheses 1 minus fraction numerator 1 over denominator 1 factorial end fraction plus horizontal ellipsis plus fraction numerator 1 over denominator 6 factorial end fraction close parentheses
    = 135 + 264 + 265 = 664

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