n youth corp have to stand in a row if all possible permutations;are equally likely. Fine the probability that 2 particular corp members stand side by side.
To find the probability that two particular corps members stand side by side in a row of n corps members, we need to count the favorable outcomes and divide it by the total number of possible outcomes.
Let's assume the two particular corps members are A and B.
First, we need to determine the total number of possible outcomes.
In a row of n corps members, there are n! (n factorial) possible permutations.
Now, let's count the favorable outcomes or the number of ways the two particular corps members can stand side by side.
To visualize this, we can group A and B together as one entity, thus reducing the number of entities by one. Now, there are (n-1)! ways to arrange these entities (when the A and B entity is treated as one). However, within this arrangement, A and B can be arranged amongst themselves in 2! ways. Therefore, the number of favorable outcomes is (n-1)! * 2!.
Finally, we can calculate the probability by dividing the favorable outcomes by the total number of possible outcomes:
Probability = (number of favorable outcomes) / (total number of possible outcomes)
= [(n-1)! * 2!] / n!
Simplifying this expression further is possible, but for now, this gives you the probability that the two particular corps members stand side by side.