How many permutations of this alphanumerical string are possible under these conditions?

Question

The string is in the format:

$N_1 N_2 L_1 L_2$

Under the following conditions:

$N_1$ and $N_2$ can be numbers 0-9, and $L_1$ and $L_2$ can be letters A-Z.

Initially, I thought it would just be $(99 x 26^2)-26=66,898$ but I have a feeling I'm missing something.

Thanks

Answer 1

As the permutations of the resulting string should all be unique, then:

• Numbers can be selected in $10\cdot 9$ ways
• Letters can be selected in $26\cdot 25$ ways

Thus there are $10\cdot 9\cdot 26\cdot 25 = 58500$ possible combinations.

EDIT

If there are no restrictions for permutations, then there are $10^2 26^2$ possible ways to construct the string.

There are 4 possibilities (in brackets is the number of unique permutations of the resulting string):

• Numbers are equal, letters are different ($\frac{4!}{2!} = 12$)
• Numbers are equal, letters are equal ($\frac{4!}{2!2!} = 6$)
• Numbers are different, letters are equal($\frac{4!}{2!} = 12$)
• Numbers are different, letters are different($4! = 24$)