New car registration plates contain two letters followed by two numerals followed by two more letters eg  AC 12 DC. Letters and numerals may be repeated.

Which of the following expressions gives the correct number of car registration plates that begin with the letter M?

A design of numberplates has a two-digit number, two letters and then another two-digit number, for example

1. How many different numberplates are possible using this design?   (1 mark)
   

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Jo can order a numberplate with ‘JO’ in the middle but will have to have randomly selected numbers on either side.

Jo’s birthday is 30 December 1992, so she would like a numberplate with either 

2. What is the probability that Jo is issued with one of the numberplates she would like?   (2 marks)
   

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Mary is designing a website that requires unique logins to be generated.

She plans to generate the logins using two capital letters from the alphabet followed by a series of numerals from 0 to 9 inclusive. All logins will have the same number of numerals. Repetition of letters and numerals is allowed.

What is the minimum number of numerals required for each login so that Mary can generate at least 3 million logins?

Justify your answer with suitable calculations.   (2 marks)