video_club_anagrams.py

import collections
from typing import Counter, List, Set, Tuple


def subanagrams(letters: Counter[str], words: Set[str], min_len=4) -> List[Tuple[str, Counter[str]]]:
    anagrams = []
    for word in words:
        if len(word) < min_len: continue
          
        rest = letters.copy()
        rest.subtract(collections.Counter(word))
        if any(n < 0 for n in rest.values()): continue  # word isn't a subset of letters
          
        anagrams.append((word, rest))
    return anagrams


def main():
    with open('/usr/share/dict/words') as f:
        words = {line.strip().upper() for line in f}
        
    anagrams = subanagrams(collections.Counter('VIDEOCLUB'), words)

    for word, rest in sorted(anagrams):
        print(word, ''.join(sorted(rest.elements())))


if __name__ == '__main__':
    main()

output looks like:

BECLOUD IV
BIDE CLOUV
BILE CDOUV
BLOC DEIUV
BLUE CDIOV
BODE CILUV
BODICE LUV
…