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15 May, 04:39

Find the number of ways to distribute six different toys to three different children such that each child gets at least one toy. The number of ways to distribute six different toys to three different children such that each child gets at least one toy is

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  1. 15 May, 08:00
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    Step-by-step explanation:

    Given that there are six different toys and they are to be distributed to three different children.

    The restraint here is each child gets atleast one toy.

    Let us consider the situation as this.

    Since each child has to get atleast one toy no of ways to distribute

    any 3 toys to the three children each. This can be done by selecting 3 toys from 6 in 6C3 ways and distributing in 3! ways

    So 3 toys to each one in 6x5x4 = 120 ways

    Now remaining 3 toys can be given to any child.

    Hence remaining 3 toys can be distributed in 3x3x3 = 27 ways

    Total no of ways

    = 120 (27)

    = 3240
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