PIN number consists of four letters, how many different PINs are possible?

Question

The personal identification number (PIN) used by a certain automatic teller machine (ATM) is a sequence of four letters.

a) How many different PINs are possible? Write the answer in exponential notation.

b) If no two letters in the PIN can be the same, how many different PINs are possible?

I am able to solve (b) by calculating: 26 nPr 4 which = 358800

but for a I not sure how to solve.

I know the answer to (a) is 456976 but don't know how to get there. Thanks for any help!

Answer 1

For (a), you can pick any of 26 letters for the first choice, any of 26 letters for the 2nd, any of 26 for the 3rd...

Answer 2

Okay I figured it out.

Since there's 26 letters in the alphabet and 4 available places. The answer is simply 26^4! xD

Answer 3

Since PIN is a sequence of 4 letters so we can fill these fours places in following ways :

1. any 1 out of 26 letters in first place.

2. any 1 out of 26 letters in second place.

3. any 1 out of 26 letters in third place.

4. any 1 out of 26 letters in forth place.

So total numbers of ways in which a PIN can be form will be :-

26*26*26*26 = $26^4$