Question

A bank password consists of two letters of english alphabet followed by two digits how many different passwards are there

Answer 1

Hi there !
Here's the answer:

•°•°•°•°•°<><><<><>><><>°•°•°•°•°

Given,
Bank Password has 2 English alphabet letters and 2 Digits

PASSWORD = [ _ ] [ _ ] [ _ ] [ _ ]

Digit - 1 & 2 are Alphabets while Digit - 3 & 4 are digits

We know,
No of alphabets = 26 ( A through z)
No. of digits = 10 ( 0 through 9)


Here,
There are 2 cases to be considered:

• CASE - 1:
WITHOUT REPETITION:

Of the 4 digits of Password,
- Digit 1 can be filled in 26 ways
- Digit 2 can be filled in 26 ways

- Digit 3 can be filled in 10 ways
-Digit 4 can be filled in 10 ways.

•°• Total No. of ways possible = 26×26×10×10 = 676× 100 = 67600


• CASE -2 :
WITH REPETITION:

Of the 4 digits of the password
- Digit 1 can be filled in 26 ways
- Digit 2 can be filled in 25 ways
(Excluding Digit 1)

- Digit 3 can be filled in 10 ways
-Digit 4 can be filled in 9 ways.
(Excluding Digit 2)

•°• Total No. of ways possible = 26×25×10×9 = 58500

•°•°•°•°•°<><><<><>><><>°•°•°•°•°

Hope it helps

Answer 2

Answer:

Using Product rule i.e., Suppose a work is done in n1 ways and n2 ways to do another work after the first work is done then there are n1.n2 ways to do the procedure.

Step-by-step explanation:

             Password

   L1       L2       L3       L4

    A        A        D         D                    A-Alphabet   D-Digit

A=26(a-z)

D=10(0-9)

There are 26*26*10*10

                =676*100

                =67600

There are 67600 ways to form the password.