<h3>Answer: 720</h3>
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Explanation:
The number 8 from "8 year old boy" can be completely ignored. In my opinion, this is an (un)intentional distraction on your teacher's part.
There are 6 toys to arrange. The order is important.
- For the first slot, there are 6 choices.
- Then the second slot has 5 choices (we cannot have a toy occupy more than one slot at a time).
- The third slot has 4 choices, and so on.
We have this countdown: 6,5,4,3,2,1
Those values multiply out to 6*5*4*3*2*1 = 720
There are 720 ways to arrange the 6 different toys. Order matters.
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An alternative approach is to use the nPr permutation formula with n = 6 and r = 6. We use a permutation because order matters.
The nPr formula is
where the exclamation marks indicate factorial. For example, 6! = 6*5*4*3*2*1 = 720.