combinations: a toy box has 6 compartments. four different toys are to be put in the box.

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mathsem

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a toy box has 6 compartments. four different toys are to be put in the box. If each compartment can hold at least 4 toys, how many arrangements are possible?

the answer is 1296 (says in back of book) but I don’t know how to get there
 
How many compartments can you choose from to place the 1st toy?
How many compartments can you choose from to place the 2nd toy?
How many compartments can you choose from to place the 3rd toy?
How many compartments can you choose from to place the 4th toy?
 
mathsem said:
a toy box has 6 compartments. four different toys are to be put in the box. If each compartment can hold at least 4 toys, how many arrangements are possible? the answer is 1296 (says in back of book) but I don’t know how to get there
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Your textbook is correct providing the compartments are also distinct (that should have been stated).
That is the number of functions from a set of four to a a set of six.
 
I am tiny bit late to this (2 years). For anyone wondering why the answer is 6^4, think of the question like this. There are 4 toys and you drop them into a random compartment in the box each time. Each time a toy has a chance to drop into one of the six compartments. This means there are 6x6x6x6 or 6^4 different solutions.
 
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