Question

One installs a new alarm system in your house and need to create a passcode that consists of 5 digits.  How many different passcodes can you create if?

• There are no restrictions?
• None of the digits can repeat
• None of the digits can be odd?
• The first digit cannot be a 0 and the last digit cannot be a 0 or 1?
• The first digit cannot be a 5 and none of the digits can repeat?

Answer 1

1)with no restrictions =N(10 choice for each) =10⁵ =100000

2)N( None of the digits can repeat ) =N(select 5 and arrange) =(₁₀P₅)=10*9*8*7*6 =30240

3)None are odd =N(5 choices for each) =5⁵ =3125

4) The first digit cannot be a 0 and the last digit cannot be a 0 or 1

=N(9 for first 10 for 2nd ,3rd and 4th and 8 choices for last) =9*10*10*10*8=72000

5)

first digit cannot be a 5 and none of the digits can repeat =N(9 choices for first, 9 for 2nd, 8for third and so on) =9*9*8*7*6=27216