Question

“n” number of cadets are needed to stand in a row. If all possible permutations are equally likely, then the probability that two particular cadets stand side by side, is?
A. 2/n
B. 1/n
C. 2/(n-1)!
D. None of these

Answer 1

Hint: Putting things in a specific order is known as a permutation. In this arrangement, the components or components of sets are organized in a linear or sequential order. In contrast to combination, where the order of the elements is irrelevant, permutation calls for a specific arrangement of the elements. The likelihood that a specific occurrence will take place at a specific time is explained by probability.

Complete step-by-step solution:
According to the given question, a total of “n” number of cadets are to be arranged in all possible orders.
So,
Therefore, We can arrange n cadets in n! a number of ways.
i.e. Total cases = n!
Now, the total number of favorable outcomes = 2! (n-1)! = 2(n-1)!
Hence, the required probability = (Total number of favorable outcomes) / (Total number of possible outcomes)
Hence, the probability is, \[\dfrac{{[2(n - 1)!]}}{{n!}} = \dfrac{2}{n}\].

Hence, option (A) is correct

Additional Information > The act of placing the items or numbers in order is known as a permutation. Combinations are a method of selecting items or numbers from a collection of items or a group of items without regard to their order. The primary difference between combinations and permutations is that combinations are various selection methods without taking sequence into consideration. Additionally, permutations are different configurations of the order. As a result, we can describe permutation as an ordered combination.

Note: Permutation refers to the possible arrangements of a set of given objects when changing the order of selection of the objects is treated as a distinct arrangement.