An urn contains $20$ balls numbered $1$ through $20$. Three of the balls are selected from the run randomly without replacement, and $X$ denotes the largest number selected. What is $P(X=18)$?
This is the method I tried however, it is incorrect, I believe that this captures the chance of selecting a specific ball?
$$1- {{19\choose 3}\over{20\choose 3}} = 0.15$$
Should I maybe consider?
$$\frac{{18\choose 3} – {17\choose 3}}{20\choose3}$$
Best Answer
If it is more recognizable for you then you could think of a bag of $20$ marbles of which $17$ have color green, $1$ has color red and $2$ have color blue. If you pick $3$ marbles, then what is the probability of picking $2$ green marbles and $1$ red marble?
Answer:$$\frac{\binom{17}2\binom11\binom20}{\binom{20}3}$$