Use of binomial probability distribution if events occur simultaneously?

I recently did a question, Numbers are selected at random, one at a time from two-digit numbers {00-99} with replacement. An event E occurs if and only if the product of the two digits of a selected number is 18. If four numbers are selected, Find the probability that the event E occurs at least 3 times.

The numbers possible are (29,36,63,92) and the ways are probability was calculated by making cases. For the case of 3 successes and one failure, binomial probability distribution formula was used for the same.

In this question it does make sense to use it sine the numbers are drawn one-by-one and with replacement. If instead say the numbers were drawn simultaneously would it still make sense to use the binomial probability distribution? Since now the order of successes and failures would not matter !?