Problema Solution
Sicily is playing a game where she is trying to guess the four digits in her friend's locker code, in any order. The digits range from 1 to 20, and none of the digits are repeated. If Sicily makes 6 guesses, what is the probability that she will make a winning guess?
Answer provided by our tutors
A formula for the number of possible permutations of k objects from a set of n is nPk = n!/(n - k)!
in our case n = 20 and k = 4
20P4 = 20!/(20 - 4)! = 20!/16! = 17*18*19*20 is the total number of possible guesses
since Sicily makes 6 guesses the probability is
p = 6/(17*18*19*20)
p = 1/19380
p = 0.0000515996 or 0.0052%