Final answer:
The probability that someone will pick exactly the 3 realtors that visited every continent out of 10 in the office is calculated using combinations and is found to be 1/120.
Step-by-step explanation:
The question asks about the probability of selecting 3 realtors who have visited every continent from a total of 10 realtors in the office, given that exactly 3 of the realtors have visited every continent.
We're looking for the probability of a specific event occurring when choosing a subset from a group.
To calculate this probability we use combinations, which measures how many ways you can choose a subset of a certain size from a larger set, without regard to the order of the elements.
The formula for combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.
Here, we need to calculate the probability of selecting all 3 travelled realtors out of the total of 10.
We use the combination formula to find the total number of ways to choose 3 realtors from 10 (which is C(10, 3)) and also calculate the number of ways to choose the 3 travelled realtors (which is C(3, 3), since there is only one way to select all of them).
To find the desired probability, we divide the number of successful outcomes by the total number of outcomes:
Probability = C(3, 3) / C(10, 3) = 1 / [10! / (3!(10-3)!)]
Probability = 1 / (10! / (3!7!))
= 1 / (10 * 9 * 8) / (3 * 2 * 1)
= 1 / (120)
= 1/120
Therefore, the probability that someone will pick exactly the 3 realtors that visited every continent is 1/120.