A license plate consists of two letters followed by two digits; for example, $MP78$. Neither the digits nor the letters may be repeated, and neither the letter $O$ nor the digit $0$ may be used. When reading from left to right, the letters must be in alphabetical order and the digits must be in increasing order. How many different license plate combinations are possible?

Guest Apr 2, 2015

#1**+11 **

Notice that, if A comes first, there are 24 ways to form a two-letter combo. {We can't use O}

And if B comes first we have 23 possibilities.

Up to the letter O, we have :

24 + 23 + 22+ .....+ 12 + 11 possibiilities

And after O, we have 10 + 9 + 8 +....+ 2 + 1 possibilities

So, the total possibilities is just (24)(25)/ 2 = 300 possibilities

And for the numbers, since 0 can't be used, we have :

8 + 7 + 6 + ......2 + 1 = (8)(9)/ 2 = 36 possibilities

So, the total ways of forming a license plate is given by ;

300 x 36 = 10,800 combos

CPhill
Apr 2, 2015

#1**+11 **

Best Answer

Notice that, if A comes first, there are 24 ways to form a two-letter combo. {We can't use O}

And if B comes first we have 23 possibilities.

Up to the letter O, we have :

24 + 23 + 22+ .....+ 12 + 11 possibiilities

And after O, we have 10 + 9 + 8 +....+ 2 + 1 possibilities

So, the total possibilities is just (24)(25)/ 2 = 300 possibilities

And for the numbers, since 0 can't be used, we have :

8 + 7 + 6 + ......2 + 1 = (8)(9)/ 2 = 36 possibilities

So, the total ways of forming a license plate is given by ;

300 x 36 = 10,800 combos

CPhill
Apr 2, 2015