# How many different codes?

#### aburchett

##### New member
An identification code is to consist of two letters followed by nine digits. How many different codes are possible if repetition is permitted?

My work: L=letter, D=digit
2 2 9 9 9 9 9 9 9 9 9
___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___
L L D D D D D D D D D

So there are 2 possible answers for the first blank, 2 possible answers for the second blank, 9 for the third, 9 for the forth, 9 for the fifth, and so on.

2*2*9*9*9*9*9*9*9*9*9
2^2*9^9=
1,549,681,956

There are 1,549,681,956 different code possibilities if repetition is permitted. Is this correct?

#### Subhotosh Khan

##### Super Moderator
Staff member
aburchett said:
An identification code is to consist of two letters followed by nine digits. How many different codes are possible if repetition is permitted?

My work: L=letter, D=digit
2 2 9 9 9 9 9 9 9 9 9
___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___
L L D D D D D D D D D

So there are 2 possible answers for the first blank, 2 possible answers for the second blank, 9 for the third, 9 for the forth, 9 for the fifth, and so on.

Assuming you are going to use english letters and there is no difference between capital letters and small letters

There are 26 different ways to fill the first position (same for the next position)

2*2*9*9*9*9*9*9*9*9*9
2^2*9^9=
1,549,681,956

There are 1,549,681,956 different code possibilities if repetition is permitted. Is this correct?

#### aburchett

##### New member
So the answer would be 26^2 * 9^9= 676 * 387,420,489= 261,896,250,564 ?