What is the probability of getting seven good lemons and three bad out thirty lemons?

The probability of getting seven good lemons and three bad lemons out of thirty lemons can be calculated using the concept of combinations. In this case, we need to choose seven good lemons and three bad lemons from a total of thirty lemons.

The total number of ways to choose seven lemons out of thirty lemons is given by the combination formula: C(30, 7) = 30! / (7! * 23!) = 10950.

The total number of ways to choose three bad lemons out of thirty lemons is given by the combination formula: C(30, 3) = 30! / (3! * 27!) = 4060.

Therefore, the total number of ways to choose seven good lemons and three bad lemons out of thirty lemons is given by the product of these two combinations: C(30, 7) * C(30, 3) = 10950 * 4060 = 44599500.

Hence, the probability of getting seven good lemons and three bad lemons out of thirty lemons is:

P(7 good, 3 bad) = (Number of ways to choose 7 good and 3 bad) / (Total number of ways to choose 10 lemons)

= 44599500 / C(30, 10) = 44599500 / 184756 = 0.241

Therefore, the probability of getting seven good lemons and three bad lemons out of thirty lemons is approximately 0.241 or 24.1%.