Question: 2014 Winter Final - 2
A password consists of 10 characters, each character being a lowercase letter or a digit. A password
must contain at least one digit and at most three digits. How many passwords are there?
(a)
none of the above
(b)
${10 \choose 1}26^9 + {10 \choose 2}26^8 + {10 \choose 3}26^7$
(c)
$10 \cdot 26^9 + 10^2 \cdot 26^8 + 10^3 \cdot 26^7$
(d)
${10 \choose 1} \cdot 10 \cdot 26^9 + {10 \choose 2} \cdot 10^2 \cdot 26^8 +$ $ {10 \choose 3} \cdot 10^3 \cdot 26^7$