Question 185458
Since "Only the digits 1 through 7 are allowed", this means that there are 7 digits available.


So you have 7 choices for the first slot. Afterwards, you have 6 choices for the second slot (since you cannot repeat digits). Then you have 5 choices for the 3rd, etc...



So we have the following:


<u>7</u>*<u>6</u>*<u>5</u>*<u>4</u>*<u>3</u>=7*6*5*4*3=2,520


So there are 2,520 different possible passwords



As an alternative, you can use a permutation to calculate the answer.