How to check if all items in a list are there in another list?

When number of occurrences doesn’t matter, you can still use the subset functionality, by creating a set on the fly:

>>> list1 = ['a', 'c', 'c']
>>> list2 = ['x', 'b', 'a', 'x', 'c', 'y', 'c']
>>> set(list1).issubset(list2)
True

If you need to check if each element shows up at least as many times in the second list as in the first list, you can make use of the Counter type and define your own subset relation:

>>> from collections import Counter
>>> def counterSubset(list1, list2):
        c1, c2 = Counter(list1), Counter(list2)
        for k, n in c1.items():
            if n > c2[k]:
                return False
        return True
   
>>> counterSubset(list1, list2)
True
>>> counterSubset(list1 + ['a'], list2)
False
>>> counterSubset(list1 + ['z'], list2)
False

If you already have counters (which might be a useful alternative to store your data anyway), you can also just write this as a single line:

>>> all(n <= c2[k] for k, n in c1.items())
True