If you are allowed to use numbers 1 - 20 and need to choose the passcode of an exact 4 digit code, how many possibilities are there?

Since in a pass code, the placement of the digits is important, therefore this means that to solve for the total number of possibilities we have to make use of the principle of Permutation. The formula for calculating the total number of possibilities using Permutation is given as:

P = n! / (n - r) !

where,

n = is the total amount of numbers to choose from = 20

r = is the total number of digits needed in the passcode = 4

Therefore solving for the total possibilities P:

P = 20! / (20 - 4) !

P = 20! / 16!

P = 116,280

Hence there are a total of 116,280 possibilities of pass codes.