Question 300277
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Order matters here.  To show that order matters here,

Let the teachers be A,B,C,D,E,F
Let the sections be 1,2,3,4.

Now take an arbitrary sample case, for instance:

B with secton 1, E with section 2, A with section 3, and C with section 4.

This is a different situation from when those same four teachers are 
positioned in a different order, say,

A with secton 1, C with section 2, E with section 3, and B with section 4.

So the number is  

"6 Position 4" = {{{6P4 = 6!/(6-4)! = (6*5*4*3*2*1)/(2*1)=(6*5*cross(2*1))/(cross(2*1))=6*5*4*3=360)}}}
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[Don't confuse that with "6 Choose 4" or "6C4" when order does not matter,
as if we were choosing a committee of 4 from the 6 teachers. Always take
a specific sample case, think of rearranging it and decide whether the
rearrangement is considered a different situation or the same situation.
Reaggarnging the members of a committee does not change the committee, but
assigning the same 4 to different sections is not the same situation.]
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Edwin</pre>