# 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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