Five people are randomly selected from 30 people, and then it is found that the height of these five people is increasing or decreasing. What is the probability that the height of the first person among these five people is the shortest among the 30 people.
My attempt:
5 people can be chosen in 30C5
29C4 - combination of all except the shortest person.
So the answer = 29C4/30C5
Just want to check to see if this is the correct way to approach this problem?
Given that there is a unique shortest person in the group of $30$, the heights of some of the others being the same or not is irrelevant.
Further, you aren't asking for the probability of the shortest person being in the group of $5$ chosen, you are asking that the first person in the group of $5$ is the shortest of $30$
That probability is simply $\dfrac1{30}$