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Find the Total Number of Ways in Which 20 Balls Can Be Put into 5 Boxes So that First Box Contains Just One Ball ?

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Question

Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?

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Solution

Any one of the twenty balls can be put in the first box. Thus, there are twenty different ways for this.
Now, remaining 19 balls are to be put into the remaining 4 boxes. This can be done in`4^19` ways because there are four choices for each ball.
∴ Required number of ways =`20xx4^19`

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Chapter 16: Permutations - Exercise 16.2 [Page 16]

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R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.2 | Q 44 | Page 16

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