Maths-
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Easy

Question

Number of ways in which 5 different toys can be distributed among 5 children if exactly one child do not get any toy

  1. 1100
  2. 1200
  3. 1300
  4. 240

The correct answer is: 1200


    therefore5 toys has to be distributed among 4 children after one of them is excluded. Which means one of them will get 2 toys.
    So this can be done is
    equals fraction numerator 5 straight C subscript 2 times cubed straight C subscript 1 cross times squared straight C subscript 1 cross times to the power of 1 straight C subscript 1 cross times 4 factorial over denominator 3 factorial end fraction times open square brackets table attributes columnalign left columnspacing 1em end attributes row cell text  asgroup  end text end cell row cell text  willbe  end text 2 comma 1 comma 1 comma 1 end cell end table close square brackets
    = 10 × 3 × 2 × 4 = 240
    Now one child can be rejected is 5 straight C subscript 1 = 5 ways
    thereforeTotal ways = 5 × 240 = 1200

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