The no of ways in which 4 distinct balls can be put into 4 boxes labelled a,b,c,d so that exactly one box remains empty is

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The no of ways in which 4 distinct balls can be put into 4 boxes labelled a,b,c,d so that exactly one box remains empty is

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Kinsley 5 days 2021-09-13T14:52:02+00:00 1 Answer 0 views 0

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    2021-09-13T14:53:25+00:00

    Answer: 162 ways

    Step-by-step explanation:

    One of four boxes should be empty. Hence any three boxes should be filled with one ball atleast.

    To choose three boxes from four, there are 3 ways possible.

    Choose 3 balls out of 4 to put one each in these 3 boxes. There are 3 ways possible for this.

    To place one ball in each of these 3 boxes, there are 6 ways possible.

    To place the remaining ball in one of the 3 boxes, there are 3 ways possible.

    Hence the total number of ways you can put these balls is:

    3 \times 3 \times 6 \times 3 = 162

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