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The number of ways of dividing 52 cards amongst four players equally, are

  1. fraction numerator 52   factorial over denominator left parenthesis 13   factorial right parenthesis to the power of 4 end exponent end fraction    
  2. fraction numerator 52   factorial over denominator left parenthesis 13   factorial right parenthesis to the power of 2 end exponent   4 rightwards arrow over short leftwards arrow   factorial end fraction    
  3. fraction numerator 52   factorial over denominator left parenthesis 12   factorial right parenthesis to the power of 4 end exponent   left parenthesis 4   factorial right parenthesis end fraction    
  4. None of these    

The correct answer is: fraction numerator 52   factorial over denominator left parenthesis 13   factorial right parenthesis to the power of 4 end exponent end fraction


    Required number of ways
    equals to the power of 52 end exponent rightwards arrow over short leftwards arrow C subscript 13 end subscript cross times to the power of 39 end exponent rightwards arrow over short leftwards arrow C subscript 13 end subscript cross times to the power of 26 end exponent rightwards arrow over short leftwards arrow C subscript 13 end subscript cross times to the power of 13 end exponent rightwards arrow over short leftwards arrow C subscript 13 end subscript
    equals fraction numerator 52   factorial over denominator 39   factorial   cross times 13   factorial end fraction cross times fraction numerator 39   factorial over denominator 26 factorial   cross times 13   factorial end fraction cross times fraction numerator 26   factorial over denominator 13   factorial   cross times 13   factorial end fraction cross times fraction numerator 13   factorial over denominator 13   factorial end fraction equals fraction numerator 52   factorial over denominator left parenthesis 13   factorial right parenthesis to the power of 4 end exponent end fraction.

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