Question

A 4-digit PIN number is selected. What it the probability that there are no repeated digits?

Answer 1

Answer:

$P(A)=0.504$ or 50.4%

Step-by-step explanation:

The probabilities constitute a branch of mathematics that deals with measuring or quantitatively determining the possibility that an event or experiment produces a certain result. The probability is based on the study of combinatorics and is the necessary foundation of statistics.

A permutation is an ordered arrangement of objects in a group, without repetitions.

A 4-digit PIN is selected. What is the probability that there are no repeated digits?

First, there are only 10 possible values for each digit of the PIN (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). The total possibles 4 PINs are $10^{4} =10000$

There's no repeated numbers and all the four numbers have to be different, which means we have to select 4 numbers out of 10 numbers. Using the permutation equation $nP_{k} =\frac{n!}{(n-k)!}$

$10P_{4} =\frac{10!}{(10-4)!}=10.9.8.7.6= 5040$

So, the probability that there are no repeated digits is:

P(A)=favorable cases/possible cases

$P(A)=\frac{5040}{10000}=0.504$ or 50.4%

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