In a certain summer school program, there are five periods in the day. Each student takes English, Math, History, Science, and Science Lab. In how many orders can a student schedule be arranged given that Science lab must immediately follow the Science class?

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In a certain summer school program, there are five periods in the day. Each student takes English, Math, History, Science, and Science Lab. In how many orders can a student schedule be arranged given that Science lab must immediately follow the Science class?

Mathematics
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Since Lab must always follow Science, you can treat them as "one class" - so you are really ordering 4 classes into 4 slots. Do you know a rule that tells you how to do that?
Have you learned something called the Fundamental Counting Rule?
yea it's basically permutations

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Right. So it's a permutation of 4 objects.
Can you explain to me why it's 4 x 3 x 2 x 1 x 1
The 4 i understand because it has to be Science no matter what
Having a hard time understanding the two 1's
Right. If you do it as a permutation of 4 from from objects, then it's 4!/0! = 4!/1 = 4! = 4*3*2*1 Is your answer showing 2 1's? I don't really think that's necessary, but here's my guess: You are ordering a series of objects with n1, n2, n3... etc choices for each phase of the series., the fundamental counting rule says that you take the product of the n's, right? So for the first class, you have 4 choices, for the 2nd class, you have 3 choices, then 2, then 1, THEN you have 1 choice for the lab - it always has to go AFTER the science class.
Personally, I think it's a slightly convuluted way of modeling it. I would rather think of the lab + class as ONE item, so you are really ordering just 4 items into 4 time slots. But I guess you could look at it as 5, it's just that the 5th item - the lab - has only 1 choice as to where it can go. lol
hmmmm kinda confusing
It would just depend on how your textbook presented this type of problem. I agree, no need for the extra x1, but then, it doesn't change the answer either. :)
so if there isnt a extra one then what would be there
I would expect the answer to be 4 x 3 x 2 x 1 If you have an answer key that gives 4 x 3 x 2 x 1 x 1, I'm not sure why the extra 1 is needed. So I'm not sure what you're asking...?
nvm thanks

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