Question

1. The company has agreed on a 9- character password format, comprised of uppercase letters, lower case letters, and digits (0-9). However, the rules specify that the first 3 characters have to be digits and the next 6 can be any upper case or lower case letter. How many possible passwords are there if: a. repetitions are allowed: b. repetitions are not allowed:

Answer 1

Answer: a) 1977060966, b) 146581344.

Step-by-step explanation:

Since we have given that

There are 10 numbers,

There are 26 lower case letters,

There are 26 upper case letters,

Since the first 3 characters have to be digits and next 6 can be upper or lower.

So, a) repetitions are allowed:

$10^3\times (26+26)^6\\\\=10^3\times 52^6\\\\=1977060966$

b) repetitions are not allowed:

$^{10}P_3\times ^{52}C_6\\\\=720\times 20358520\\\\=146581344$

Hence, a) 1977060966, b) 146581344.