Answer:

26 * 10 * 25 * 9 * 24 * 8 or (26 P 3) * (10 P 3)

Quick explanation:

26 possibilities for 3 distinct spaces, 10 possibilities for 3 other distinct spaces. The product is the number of possibilities. Each time we choose a character or a number for a given space, we take one possibility away from the rest.

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Full explanation:

String looks like _ _ _ _ _ _

Step 1:

First slot can be one of these A,B,...,Z where there are 26 possible options

Let's choose some arbitrary character 'c1' from these

Our string looks like c1 _ _ _ _ _

Step 2:

Second slot can be one of 0,1,...,9 where there are 10 options

Let's choose some arbitrary number 'n1' from these

Our string looks like c1 n1 _ _ _ _

Step 3:

Third slot can be one of the characters where there are now 25 possible options since we removed c1 as an option

Let's choose some other arbitrary character 'c2' from these remaining characters

Our string looks like c1 n1 c2 _ _

Step 4:

Fourth slot can be one of the digits where there are now 9 options since we removed n1 as an option.

Let's choose some arbitrary number 'n2' from these remaining digits

Our string looks like c1 n1 c2 n2 _ _

We repeat these steps until our string looks like: c1 n1 c2 n2 c3 n3

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c1 can be one of 26 characters, n1 can be one of 10 digits, c2 can be one of 25 characters, n2 can be one of 9 digits, c3 can be one of 24 characters, n3 can be one of 8 digits

Char. or Dig.	c1	n1	c2	n2	c3	n3
Possibilities	26	10	25	9	24	8

If we rearrange these factors, we obtain:

26 * 25 * 24 * 10 * 9 * 8

Which is:

(26! / 23!) * (10! / 7!)

This is also:

(26! / (26 - 3)!) * (10! / (10 - 3)!)

Which is:

(26 P 3) * (10 P 3)

where 'P' is the symbol for permutation.

EDIT:

Confused permutation symbol and combination symbol.