You have a bag containing 26 tiles, each imprinted with one letter of the alphabet. if you pick out 5 tiles, what is the probability that they are a, e, i, o, and u in that order? a. 1/26 b. 5/26 c. 1/65,780 d. 1/7,893,600

The answer is choice D:  here is why!

Probability of an event is defined by the ratio comparing the number of things you want to have happen compared to the total number of possibilities for that event.  Here we only have one thing we want to have happen.. when we draw the 5 chips we want a,e,i.o, and u in that specific order.  So you can see the first number in our ratio is " 1 ".  Now the second number is a bit more tricky.. We have to calculate how many possible arrangements of drawing 5 letters out of 26 there are... think of it this way... compare this to a race where you're awarding 1st through 5th place ribbons for the first 5 runners to finish out of a group of 26 runners..

Well, how many choices would be possible of a first place ribbon?  You guessed it... 26.. now how many choices do we have left for a 2nd place ribbon?  Yep  25!  then 24 for 3rd, 23 for 4th, and 22 for 5th.  This is exactly like drawing a,e,i,o, and u in that specific order.  Now the fundamental counting principle states that if you want to know the total number of outcomes possible from a series of choices, you simply multiply the number of options for each choice, decision, or event(like drawing a chip with a letter on it...  ha!) 

So let's just multiply the number of options we have for each chip drawn.
26x25x24x23x22 = 7,893,600

Therefore, our probability:  P(a,e,i,o,u in order) = 1/7,893,600