Frequencies in unordered cartesian products

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This is a novice question. If I have an unordered cartesian product of some list with a repeat sequence, how can I calculate the frequency with which a member of that list occurs in the combinations?

For example given the list:

list = {1,2,3,4}

The unordered cartesian product with a repeat length of 3 should give:

(1,1,1),(1,1,2),(1,1,3)........(4,4,4)

How can I calculate the number of times 1 appears at least once in this set? If I change this to at least twice can this be done? I was looking around for a formula but could not find one. Thanks