156 With reference to Exercise 155 in how many different way

1.56 With reference to Exercise 1.55, in how many different ways can the bakery distribute the 12 apple pies of each of the six food banks is to receive at least one pie?

Solution

Total no of apples in the bakery =12

Let us assume they are identical.

As each apple to be given to each food bank, first 6 apples can be distributed each to them.

Now we are left with 6 apples and they can go to any of the 6 food banks.

I apples can be distributed in 6 ways, to any of the 6

II also can be distributed in 6 ways, to any of the 6

III , Iv , v , vi also

Hence total no of ways = 6x6x6x6x6x6=

= 6⁶

= 46656 ways.