Question

Password consists of five characters: one lowercase letter and four digits 0 – 9.

1. How many possible combinations for the password are there if digits can be repeated?
2. How many possible combinations for the password are there if digits can not be repeated?
3. What is a percentage of passwords with repeated digits?

Answer 1

Given that 5 Char password.

Here condition is 1 lower case letter and 0-9 numbers

i.e. 26 letters and 10 numbers...

a.

N(password are there if digits can be repeated) = 5 * 26* 10*10*10*10 = 1300000

here char canbe fit at any place of char,,...(5 C 1) is the selection for the char place...

once char place is fixed we can fill with any alphabet...

=(5 C 1) * 26

for remaining four digits every digit have 26 options because repeatation is allowed.

= 10*10*10*10

b.

number Repeatation is not allowed.

N(password are there if digits can be repeated) = 5 * 26* 10*10*10*10 = 1300000

here char canbe fit at any place of char,,...(5 C 1) is the selection for the char place...

once char place is fixed we can fill with any alphabet...

=(5 C 1) * 26

for remaining 4 char. first one have 10 options. for 2nd place we have only 9 options,,bcs repeatation is not allowed.

number selection = 10*9*8*7

total slection = 5 * 26 * 10 *9* 8 * 7 = 655200

c.

% of repeate = 655200/1300000 = 0.504