   SEARCH HOME Math Central Quandaries & 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. Hi,

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,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.