Calculate the possible combinations for an eight-character password Can any when one help me in this question: 
Calculate the possible combinations for;


*

*An eight-character password consisting of upper- and lowercase letters and at least one numeric digit $(0–9)$?

*A ten-character password consisting of upper- and lowercase letters and at least one numeric digit $(0–9)$?
Thanks 

For both cases, you need to find the total number of combinations and then subtract the number of ones that don't match.
For reference, there are 26 capital letters, 26 lowercase letters, and 10 digits.
For the first case, let $N_8$ be the total number of 8 character passwords and $W_8$ be those without digits.
$$
N_8 = \binom{26+26+10}{1}^8 = \binom{62}{1}^8 = 62^8 \\
X_8 = \binom{26+26}{1}^8 =\binom{52}{1}^8 = 52^8
$$
Now let $D_8$ be the number of 8 character passwords with at least one digit.
$$
D_8 = N_8 - X_8 = 62^8 - 52^8 \approx 1.64 * 10^{14}
$$
Do the same for the second case:
$$
N_{10} = \binom{62}{1}^{10} = 62^{10} \\
X_{10} = \binom{52}{1}^{10} = 52^{10} \\
D_{10} = N_{10} - X_{10} = 62^{10} - 52^{10} \approx 6.95 *10^{17}
$$
