### Instruction: If three people are selected at random from a group of seven men and three women, what is the probability that at least one woman is selected? Express your answer as a common fraction.### Response: To find the probability of at least one woman, I can use the complement rule and subtract the probability of no women from 1.
The probability of no women is the same as the probability of selecting only men.
There are 10 people in total, so the number of ways to choose 3 of them is 10 choose 3, which is 120.
The number of ways to choose 3 men from 7 men is 7 choose 3, which is 35.
So the probability of selecting only men is 35/120, which simplifies to 7/24.
Therefore, the probability of selecting at least one woman is 1 - 7/24, which is 17/24.