Question

A car licence plate consists of 7 characters. The first 4 characters arenumerals from 0 to 9. The last 3 characters are letters excluding I, O,and X. How many different licence plates are possible?

Answer 1

Let's draw a little diagram to help us answer this question:

• The first box can be the numerals ,0 to 9,, that is ,10 digits,.

,

• The second box can be the numerals ,0 to 9,, that is ,10 digits,.

,

• The third box can be the numerals ,0 to 9,, that is ,10 digits,.

,

• The fourth box can be the numerals ,0 to 9,, that is ,10 digits,.

Then,

• Fifth box can have all the letters of the alphabet (26 of them) EXCEPT ,I, O, and X. ,That is 26 - 3 = ,23 letters,.

,

• Sixth box can have all the letters of the alphabet (26 of them) EXCEPT ,I, O, and X. ,That is 26 - 3 = ,23 letters,.

,

• Seventh box can have all the letters of the alphabet (26 of them) EXCEPT ,I, O, and X. ,That is 26 - 3 = ,23 letters,.

So, we can now see the rough diagram below with the number of elements in each of the 7 boxes:

From fundamental rule of counting, we need to multiply all of these to get the number of different licence plates possible. Shown below:

`10*10*10*10*23*23*23=121,670,000`Answer121,670,000