Answer:
a) [tex]6.04661760*10^8[/tex]
b) 0.27778
Step-by-step explanation:
a)
There are 26 lowercase letters and 10 digits.
The character that must be a digit can be generated in 10 different ways and the others, in 26+10=36 different ways.
Since the password is 6 characters long, by the Fundamental Rule of Counting there are
10*36*36*36*36*36 = 604,661,760
In scientific notation this number can be expressed as
[tex]6.04661760*10^8[/tex]
b)
By the Fundamental Rule of Counting, there would be
[tex]36^6[/tex]
different combinations of 6 characters, but only the number computed in a) are valid combinations, so the probability of generating a valid password is
[tex]\displaystyle\frac{10*36^5}{36^6}=\displaystyle\frac{10}{36}=0.27778[/tex]
