Choosing a Password

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To make an account in a site, the person need to choose a password formed by four characters in which two characters must be numbers and the other two must be an alphabet (CAPITAL, small or Both). The numbers and alphabets can be placed in a random order, and one CAPITAL letter is different from a small letter .

For example, these three passwords are valid: K2E1 , K0a3 or 8up3 , but the next three aren't: LtE1 , K013 or lUp3 .

What is the total number of password that we can form with this rules?

(The english alphabet has only 26 letters)

1 0 2 ⋅ 2 6 2 ⋅ 4 ! 2 ! ⋅ 2 ! 10^2\cdot26^2\cdot\frac{4!}{2!\cdot2!} 1 0 2 ⋅ 2 6 2 10^2\cdot26^2 1 0 2 ⋅ 5 2 2 ⋅ 4 ! 2 ! ⋅ 2 ! 10^2\cdot52^2\cdot\frac{4!}{2!\cdot2!} 1 0 2 ⋅ 5 2 2 ⋅ 4 ! 2 ! 10^2\cdot52^2\cdot\frac{4!}{2!} 1 0 2 ⋅ 5 2 2 10^2\cdot52^2

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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