Question

An anonymous caller told the police that he saw a hit and run incident and had briefly seen 

the number plate of the car. He knew that the number plate started with two letters – a B 

and an E – but could not remember the order. After the letters were four digits – 3, 4, 8 and 

9 – but again he could not remember the order. The four numbers were followed by the 

letter V. How many number plates will the police have to check to be sure of including the 

car involved in the hit and run incident?

Answer 1

The number plate consist of 7 parts

The first two letters make $2*1 =2$ options

The following four numbers make $4*3*2*1=24$ options

the following letter is certainly V

So, there is $2*24*1=48$ possabilities