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Question

A California license plate starts with a digit other than 0 followed by three capital letters followed by three digits (0 through 9). How many different California license plates are possible?

How many different Cali license plates start with a 5 and end with a 9?

How many different Cali license plates have no repeated symbols (all the digits are different and all the letters are different? 

 

 

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answers:

158,184,000

1,757,600

70,761,600

Answer 1

The counting principle says that you can take the number of ways that each individual event can occur,,,,and multiply them.

So

a) 9*26*26*26*10*10*10=158,184,000

b) 1*26*26*26*10*10*1 =1,757,600

c) 9*26*25*24*9*8*7 =70,761,600

 

For Part c, since I had 9 choices for the first number, that leaves me 9 choices for the number in the fourth slot....and then i"ve already used 2 numbers, leaving me with 8 numbers for the next slot and 7 for the final slot. For the letters, I had 26 choices for the first, but since ai used one and can't repeat, I have 25 for the net....and now that I used 2 letters already, I have 24 choices for the last letter.

 

Hope this helped.