Answer: There are 13 gamblers who played exactly two games.
Step-by-step explanation:
Since we have given that
Number of gamblers played black jack, roulette and poker = 5
Number of gamblers played roulette and poker = 8
Number of gamblers played black jack and roulette = 11
Number of gamblers played only poker = 12
Number of gamblers played poker = 24
Number of gamblers who played only roulette and poker is given by
Number of gamblers who played only black jack and roulette is given by
Number of gamblers who played only poker and black jack is given by
So, the number of gamblers who played exactly two games is given by
Hence, there are 13 gamblers who played exactly two games.