A class with n kids lines up for recess. The order in which the kids line up is random with each ordering being equally likely. Probability that Celia is at first in line is 1/n.
<h3>What is probability and permutation? </h3>
Probability refers to potential.
A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1.
Probability of an event occurring is given by
P(E) = (No. of favourable outcomes)/ (No. of total outcomes)
Permutation: When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection.
Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems. Formula of permutation is given as
![^{n}P_{r} = \frac{n !}{(n - r) !}](https://tex.z-dn.net/?f=%5E%7Bn%7DP_%7Br%7D%20%3D%20%5Cfrac%7Bn%20%20%21%7D%7B%28n%20-%20r%29%20%21%7D)
For finding probability of Celia at first position in class of n kids we will do permutation and then apply formula of probability.
Total ways of arranging n kids = n!
But is we fix Celia at first position then ways of arrangement will be (n - 1)!
![P(E) = \frac{(n - 1)!}{n!} = \frac{1}{n}](https://tex.z-dn.net/?f=P%28E%29%20%3D%20%5Cfrac%7B%28n%20-%201%29%21%7D%7Bn%21%7D%20%3D%20%5Cfrac%7B1%7D%7Bn%7D)
n! = n (n - 1) (n - 2)
To know more about probability, follow link: brainly.com/question/10734660
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