How many different number plates can you create by using 1 letter and 4 numbers?

Question

How many different number plates can you create by using 1 letter and 4 numbers?

 

My answer is

26 X 10 X 10X 10 X 10 but my book answer was

 

26 X 10 X 10X 10 X 10 X 5

 

 

 

Answer 1

1 letter and 4 digits give the following

the first character can be a letter and the others are digits...

26*10*10*10*10

the second character can be a letter...

10*26*10*10*10

the third character can be a letter...

10*10*26*10*10

fourth character a letter...

10*10*10*26*10

fifth character a letter...

10*10*10*10*26

the combination of 4 10s and 1 26 appears 5 times

26*10*10*10*10*5 is the answer

1,300,000 license plates

Answer 2

The book is correct. 26 x 10 x 10 x 10 x 10 would give you the number of combinations where the letter is in a particular spot (first, second, third, etc.).

 

Because the order of the letters and numbers matters (A1234 is a different license plate from 1A234), we also need to account for the way that they are ordered. There are 5 options for where the letter can be placed, so the correct answer is that there are 26 x 10 x 10 x 10 x 10 x 5.

 

i hope this helps!

 

Andy

Answer 3

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