Suppose there are numbers $\{1, \ldots, 10\}$

You pick one at random, call it $i$

Then $i$ is a Uniform random variable (https://en.wikipedia.org/wiki/Discrete_uniform_distribution), $i \sim U\{1, 10\}$. Then you use it for SGD by taking the gradient of the $i$th loss.

What about minibatch $B$?

In this case you are sampling several numbers from $\{1, \ldots, 10\}$ without replacement. Suppose you are assuming a batch size of $2$.

The probability of sampling the first one is $1/10$, the second one is $1/9$.

Then the random vector $B$ follows some joint distribution. Does anyone know how to model this joint distribution? I feel like this is something super obvious (thinking in the line of products of uniform distribution - not sure how to express this mathematically).