Answer:
![Probability = \frac{1}{5040}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cfrac%7B1%7D%7B5040%7D)
Step-by-step explanation:
Given:
Number of students: 30
Student ID = 4 digit (0 - 9 without repetition within an ID)
Required:
Calculate the probability that one of those ID numbers is 9876?
Step 1: First we calculate the total possible IDs.
To do this, we make use of the permutation formula; We're using this formula because the question says assign
Hence, Number of possible IDs is as follows;
![^{n} P_{r}](https://tex.z-dn.net/?f=%5E%7Bn%7D%20P_%7Br%7D)
Where n = digit 0 - 9 = 10 digits
r = 4 digits
becomes ![^{10} P_{4}](https://tex.z-dn.net/?f=%5E%7B10%7D%20P_%7B4%7D)
![^{10} P_{4} = \frac{10 * 9 * 8 * 7 * 6!}{6!}](https://tex.z-dn.net/?f=%5E%7B10%7D%20P_%7B4%7D%20%3D%20%5Cfrac%7B10%20%2A%209%20%2A%208%20%2A%207%20%2A%206%21%7D%7B6%21%7D)
![^{10} P_{4} = 10 * 9 * 8 * 7](https://tex.z-dn.net/?f=%5E%7B10%7D%20P_%7B4%7D%20%3D%2010%20%2A%209%20%2A%208%20%2A%207)
![^{10} P_{4} = 5,040](https://tex.z-dn.net/?f=%5E%7B10%7D%20P_%7B4%7D%20%3D%205%2C040)
Step 2: Calculate the required probability
Probability is calculated as number of required outcomes divided by number of total outcomes
There are only 1 possibility of having a 9876 out of a total of 5,040
Hence, the probability of having one of those ID numbers as 9876 =
![Probability = \frac{1}{5040}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cfrac%7B1%7D%7B5040%7D)