Maths-
General
Easy

Question

The number of ways in which a mixed double game can be arranged amongst nine married couples so that no husband and his wife play in the same game, is equal to:

  1. 9 C subscript 2 end subscript. to the power of 7 end exponent C subscript 2 end subscript    
  2. 9 C subscript 2 end subscript. to the power of 7 end exponent C subscript 2 end subscript. to the power of 2 end exponent C subscript 1 end subscript    
  3. 9 P subscript 2 end subscript. to the power of 7 end exponent P subscript 2 end subscript    
  4. 9 P subscript 2 end subscript. to the power of 7 end exponent P subscript 2 end subscript. to the power of 2 end exponent P subscript 1 end subscript    

The correct answer is: 9 C subscript 2 end subscript. to the power of 7 end exponent C subscript 2 end subscript. to the power of 2 end exponent C subscript 1 end subscript


    First of all two men can be selected in 9C2ways. Thereafter 2 women can selected in 7C2 ways (as wives of selected men are not be selected). And finally they can be paired up in 2C1 ways.
    Thus total ways = 9 C subscript 2 end subscript. to the power of 7 end exponent C subscript 2 end subscript. to the power of 2 end exponent C subscript 1 end subscript

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