No of distinct combinations of non distinct elements

Question

Example: Given that there are $5$ places that has to be filled with distinct values,, they come from $5$ different bags that contains distinct elements viz $\{1,2,3,5\} ,\{1,2,4\},\{1,3,5\},\{2,3\},\{2\}$ (each bag contain distinct element but two bags may contain same elements). What are the total number of combinations and what is the generalized formula ?

Answer 1

You seem to say that you want to take an element from each ordered bag.

By what I interpret form what you say, you want an element from $S_1\times S_2\times\ldots\times S_n$.

There are $\vert S_1\vert ·\vert S_2\vert ·\ldots ·\vert S_n\vert$ such elements.

In your case, $4·3·3·2·1 = 72$