Question

Imagine that you need to create a passcode that consists of 6 numbers.  How many different pin codes can you create if:

1. There are no restrictions?
2. None of the numbers can repeat?
3. None of the digits can be even?
4. The first digit cannot be a 0 or 2 and the last digit cannot be a 0 or 1?
5. The first digit cannot be 5 and none of the digits can repeat?

Answer 1

a) No restrictions:

Number of different pins = 10*10*10*10*10*10 = 1000000

b) None of the digits can repeat:

Number of different pins = 10*9*8*7*6*5 = 151200

c) None of the digits can be even:

Number of different pins = 5*5*5*5*5*5 = 15625

d) The first digit cannot be a 0 or 2 and the last digit cannot be a 0 or 1:

Number of different pins = 8*10*10*10*10*8 = 640000

e) The first digit cannot be 5 and none of the digits can repeat:

Number of different pins = 9*9*8*7*6*5 = 136080