Suppose that in a certain state, all automobile license plates have three letters followed by four numerical digits. Two letters may never be used (I, O). How many license plates are possible in which no letter or number is repeated?

Question

zepdrix · Answer

Ooo I remember doing this exact question earlier in the semester,
lemme see if I can find my notes :d

zepdrix · Answer

Oh I guess it was a little different >.< hmm

zepdrix · Answer

|dw:1445468625618:dw|

anonymous · Answer

Yeah, I'm reading through this chapter on "Combinatorics," now. Examples are always good, though. I got a B on my last test thanks to you guys at OS :D

zepdrix · Answer

Oo nice :)

zepdrix · Answer

So for the first slot,
we have 10 options, ya? 0 through 9

anonymous · Answer

I follow your logic so far

zepdrix · Answer

Woops I read it backwards :) haha
Letters come first.

zepdrix · Answer

So the first slot has the entire alphabet available to it,
with a couple of restrictions.

zepdrix · Answer

No I and no O.
So 24 options, ya?

zepdrix · Answer

|dw:1445468871739:dw|

zepdrix · Answer

Alphabet is 26 letters.
26 - I - O = 24

anonymous · Answer

No problem

zepdrix · Answer

How bout the next slot?
We've used up a letter, we can't repeat any numbers or letters.
So now only 23 are available.

zepdrix · Answer

|dw:1445469075083:dw|And similarly for the third slot, we've used up another of our letters.