Math CentralQuandaries & Queries


Question from Brijanshu:

I have a lock that contain only four no. 6,7,8 & 9 . How many possible password of four digit containing these Number.


Are you allowed to have repeating digits? For example are 6666 and 7867 legitimate passwords? If so then you have $4$ choices or the first digit, $4$ choices fro the second digit and the same for the third and fourth digits so there are $4 \times 4 \times 4 \times 4$ possible passwords.

If you are not allowed to repeat digits then you still have $4$ choices for the first digit but once you have made a choice you only have $3$ choices for the second digit. After choosing the first two digits you only have $2$ choices for the third digit and then only $1$ choice for the final digit. Hence with this restriction there are $4 \times 3 \times 2 \times 1$ possible passwords.

I hope this helps,

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