There are k sets of numbers : {0,1,2,….,m1}, {0,1,2,……..,m2}, …………,{0,1,2,………,mk}

Such that m1<m2<………<mk.

1. How many combinations of k elements can be made taken 1 element from each set such that each set has all distinct elements (no two elements are equal) ?

2. What is the probability that any two sets will have at least one element common ?

(Please provide procedure and explanation)

I think the answer given by Plato is the number of permutations, but I am looking for the number of combinations i.e., the sets with all elements same (although in different order) will be treated as one.

AND Plz mention the rule/formula name with explanation so that I can learn them