Does "The company sends each of them to one of these cities at random" necessarily mean each is sent to a distinct city here?

Question

I'm doing a math problem and I'm getting two different answers based on the interpretation of a particular sentence. The question is:

Sanjay, Ajay, and Anushka are employees of a company that has branches in Chennai, Bangalore, and Mumbai. The company sends each of them to one of these cities at random. Let X be a random variable that denotes the number of employees assigned to their favorite cities. If Chennai, Bangalore, and Mumbai are the favorite cities of Sanjay, Ajay, and Anushka, respectively, then find X's possible values.

My interpretation of the line in bold is that "two or more employees can end up in one city". But I'm confusing it with "each of the three employees gets sent to a distinct city". These two interpretations give two different answers. What is a reasonable interpretation of this sentence?

Answer 1

The company sends each of them to one of these cities at random.

I would say you should interpret it the first way, not the second way: it is possible for two or even three employees to end up in the same city. To interpret it otherwise is to fall victim to the gambler's fallacy. If the distribution is truly random, whether or not the second person goes to Chennai has nothing to do with whether or not the first person went to Chennai.

If the person who wrote the question meant that only one person would go to each city, they should have said that. Note how a subtle change in word order could make it so:

The company sends one of them at random to each city.

In the original sentence, the employees are selected one-by-one and sent to a random city; a single city can hold more than one employee. In my modified sentence the cities are selected one-by-one and an employee is sent to each; because an employee cannot be in more than one city at once, each city gets only one employee. Note that by the time you get to the last city, the assignment is no longer random!

Answer 2

As it stands, the correct interpretation should be that two or more employees can end up in one city.

I agree that this math question could be worded better by the setter, to remove any ambiguity.

Answer 3

I do think it is badly phrased, and my interpretation was the opposite of the other answers here. My feeling is not based on any grammatical rule of English, but on my sense of what makes a good question of maths and what makes sense for a company do to do.

Firstly, I wonder why the questioner wrote "to one of these cities"? Since you can't go to two cities at the same time why was it necessary to write "one".

Secondly, It doesn't make much sense for a company to send two representatives to the same city.

Thirdly, I think the mathematical problem is more interesting if you treat it as random permutation (I don't see a mathematical problem here with "random", you are sampling at random from the space of permutations on three items)