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?
+128474 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
+128474 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
