SOLUTION: A standard license plate has six spaces for either numbers or letters to be engraved: If you are allowed to use numbers OR letters in each slot, how many different license plates

Algebra ->  Permutations -> SOLUTION: A standard license plate has six spaces for either numbers or letters to be engraved: If you are allowed to use numbers OR letters in each slot, how many different license plates       Log On


   

Question 143959: A standard license plate has six spaces for either numbers or letters to be engraved:
If you are allowed to use numbers OR letters in each slot, how many different license plates are possible to make (repeating allowed)?
How does this number change if you were restricted to the following constraint:
The first three slots can only be letters, and the second three slots can only be numbers (you can repeat).
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Assume number 0-9 and letters A-Z (caps only)
Then you have 10 numbers and 26 letters
Watch this video, pay attention to the ones near the end. http://collabvsl.wetpaint.com/page/Basic+Probability
You have 36 choices and a license plate with 6 spaces
XXX-XXX
36* 36*36*36*36*36 = 36%5E6
How does this change if the plates look like
###-CCC (# is number and A is letter)
10*10*10 * 26*26*26 = 10%5E3+%2A+26%5E3
If the letters are allowed to be a-z, A-Z or include any other special characters (like !* or some such), then the number of letter goes up. The same process applies. The exponents will stay the same, but the base will go up accordingly.
make sense?