In how many ways can 5 different mangoes, 4 different oranges & 3 different apples be distributed among 3 children such that each gets atleast one mango?

Solution :

5 different mangoes can be distributed by following ways among 3 children such that each gets at least 1 :

Total number of ways : (\(5!\over 3!1!1!2!\) + \(5!\over 2!2!2!\)) \(\times\) 3!

Now, the number of ways of distributing remaining fruits (i.e. 4 oranges + 3 apples) among 3 children = \(3^7\) (as each fruit has 3 options).

Therefore, Total number of ways = (\(5!\over 3!2!\) + \(5!\over {(2!)}^3\)) \(\times\) 3! \(\times\) \(3^7\)

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