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 

assuming repetition allowed for an eight digit password 
you need one lower case which is $^{26}C_1$ and you need one upper case which is $^{26}C_1$ and you need one digit which is $^{10}C_1$ 
so we got $3$ we need another $5$ letters or numbers and repetition allowed and we have $62$ choices for each of the $5$ remaining characters 
so $\space ^{26}C_1 \cdot \ ^{26}C_1 \cdot \ ^{10}C_1\cdot \ (^{62}C_1)^5$
so for a $10$ letter password same thing first $3$ steps which is you need one lower case which is $^{26}C_1$ and you need one upper case which is $^{26}C_1$ and you need one digit which is $^{10}C_1 $
so we got $3$ we need another $7$ letters or numbers and repetition allowed and we have $62$ choices for each of the $7$ remaining characters 
so $ \ ^{26}C_1 \cdot \ ^{26}C_1 \cdot \ ^{10}C_1 \cdot \ (^{62}C_1)^7$
