# Number Probability

#### Tsrnc2

##### New member
My bank has a policy of disallowing certain pin numbers. Pins are the standard 4 digits. Pins that have all the same digit (1111), a sequence of digits forward or reverse (1234, 4321), as well as pins that start with 19 or 20 (1999) are disallowed. A 4 digit pin has 10,000 possible pins minus those disallowed. My questions is how many allowed pin possibilities exist?

#### Subhotosh Khan

##### Super Moderator
Staff member
My bank has a policy of disallowing certain pin numbers. Pins are the standard 4 digits. Pins that have all the same digit (1111), a sequence of digits forward or reverse (1234, 4321), as well as pins that start with 19 or 20 (1999) are disallowed. A 4 digit pin has 10,000 possible pins minus those disallowed. My questions is how many allowed pin possibilities exist?
How many 4-digit numbers are there with all four numbers same (e.g. 1111 or 7777, etc.)?

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#### pka

##### Elite Member
My bank has a policy of disallowing certain pin numbers. Pins are the standard 4 digits. Pins that have all the same digit (1111), a sequence of digits forward or reverse (1234, 4321), as well as pins that start with 19 or 20 (1999) are disallowed. A 4 digit pin has 10,000 possible pins minus those disallowed. My questions is how many allowed pin possibilities exist?
We cannot have $$\displaystyle (XXXX)$$ where $$\displaystyle X$$ is digit. So how many are there?

Let's see, we cannot have $$\displaystyle (19XY)$$ where $$\displaystyle X~\&~Y$$ are digits. So how many are there?
Now we need to double that number. Why is that?

How many increasing strings of four are there? Did you include $$\displaystyle \large\bf 0123~?$$
Now we need to double that number. Why is that?