I am interested in probability to win some kind of bingo game. Am I right with my calculation?

Description: We have 48 numbers from 1 to 48. From that set we choose 6 numbers before game starts. After that, game starts and 31 numbers are chosen from beginning set of 48 numbers. What is probability to win the game, to win the game all 6 number must be drown-out?

Solution: 6 numbers are chosen, number of combinations involving these 6 numbers are ${42 \choose 25}$. Total number of combinations are ${48 \choose 31}$. From these assumptions we calculate probability to win game as: $\frac{42 \choose 25} {48 \choose 31}$


That is absolutely correct. Assuming the $6$ numbers are chosen, there are $42$ remaining numbers from which you choose $25$.


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