If Sam, Tim and 10 other people are randomly positioned in a queue, then what is the probability that Sam and Tim will be positioned next to each other?A.1112B.15C.16D.110E.112Next PreviousEnd Review  Review Screen

To find the probability that Sam and Tim will be positioned next to each other in the queue, we need to consider the total number of possible arrangements where they are next to each other, divided by the total number of possible arrangements of all the people.

First, let's consider the total number of possible arrangements of all the people. Since there are 12 people in total, the number of possible arrangements is 12!.

Now, let's consider the total number of possible arrangements where Sam and Tim are next to each other. We can treat Sam and Tim as a single entity, which means there are 11 entities to arrange (Sam and Tim together, and the other 10 people). The number of possible arrangements of these 11 entities is 11!.

However, within this arrangement, Sam and Tim can also switch positions, so we need to multiply the result by 2.

Therefore, the total number of possible arrangements where Sam and Tim are positioned next to each other is 2 * 11!.

Finally, we can calculate the probability by dividing the number of favorable outcomes (arrangements where Sam and Tim are next to each other) by the total number of possible outcomes (all possible arrangements).

Probability = (2 * 11!) / 12!

Simplifying this expression, we get:

Probability = 2/12 = 1/6

So, the probability that Sam and Tim will be positioned next to each other is 1/6.

Therefore, the correct answer is not listed among the options provided.