SOLUTION: Students are given 5-digit passwords for their accounts on the school’s computer system. If no numbers can be repeat, what is the probability that a student’s password is 93152
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Question 1157548: Students are given 5-digit passwords for their accounts on the school’s computer system. If no numbers can be repeat, what is the probability that a student’s password is 93152?
I want it in details please (explain it) Answer by ikleyn(52785) (Show Source):
Let's consider these 5-digit codes with no repetitions.
In the left-most position, any of 10 digits can be placed (the problem does not prohibit 0 in this position). It gives 10 options.
In the next position from the left, only one of remaining 9 digits can be placed (9 options).
In the 3-rd position from the left, only one of remaining 8 digits can be placed (8 options).
. . . And so on . . .
In all, there are 10*9*8*7*6 = 30240 such codes.
The specific code 93152 is unique. It is only one among 30240 all possible codes.
Therefore, the probability to randomly select this code is .
