Math CentralQuandaries & Queries


Question from Rob:

If there is a 4 digit passcode with only 6 punch in symbols, how many possibilities are there and what are they?
symbols are: Y, X, RB, RT, LB, LT. Please get back to me, thanks for your time and help.

Hi Rob.

It depends on whether duplicates are allowed. For example, is Y, X, LT, X allowed?

It also depends on whether order is important. Is Y, X, LT, RT different from RT, Y, X, LT?

Assuming the answers to both question are Yes, you have 6 choices for each of the four positions, so the number of possibilities is 6 x 6 x 6 x 6.

If duplicates are not allowed, then you have 6 choices for the first symbol, 5 for the next, etc. So the number of possibilities is 6 x 5 x 4 x 3.

If order is not important, you have to weed out duplicates. The number of duplicates is the number of ways of arranging 4 things: 4 x 3 x 2 x 1 . So you would divide the number of possibilities by 24.

Stephen La Rocque.

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS