The registration number of the vehicle consists of two letters, three numbers and two letters. How many registration numbers can we form if we use 25 letters.
is this using the combinations theory? or a factorial of 25. I understand that there is only 10 numbers that can be used so maybe 25! x 10!?
Think about it as placeholders:
$$\underbrace{\_ \space \_ }_\text{letters} |\underbrace{ \_ \space \_ \space \_ }_\text{numbers} |\underbrace{ \_ \space \_ }_\text{letters}$$
I am assuming we can repeat digits and repeat letters, as it isn't stated that we can't.
We are using $25$ letters, and there are $10$ digits (0 through 9)
We start with two letters, so we have $$ 25 \times 25 \times \_ \space \_ \space \_ | \_ \space \_ $$ Once we look at the spots that we want a number, we have $10$ options there, so we plug those in and now have $$ 25 \times 25 \times 10 \times \_ \space \_ | \_ \space \_ $$
See if you can use this to finish the problem.