Question 1203275
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Part (a)


There are 9 choices in the first slot, then 8 for the next, and so on. 


9*8*7*6*5*4*3*2*1 = <font color=red>362,880</font> different ways to arrange the letters of FACETIOUS.


For more information, search out "factorial".


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Part (b)


I'm assuming the "5" should be "S"


We have F locked in the first slot and S locked in the last slot.


There are 2 letters locked in place. 
That leaves 9-2 = 7 letters left to arrange in 7 slots.


7*6*5*4*3*2*1 = <font color=red>5,040</font> different ways to arrange the letters of FACETIOUS such that the "word" begins with F and ends with S.
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