easy Probability

One Given Increasing

A release-checked easy problem for training Combinations and Permutations, Conditional Probability.

Question

Fix positive integers $1 \leq r \leq n$. $r$ integers are selected one-at-a-time without replacement at random from $[n] = \{1,2,\dots, n\}$. Given that the numbers are in increasing order, find the probability that $1$ was selected. Report the answer when $r = 5$ and $n = 100$.

Practice focus

This Probability problem is tagged Combinations and Permutations, Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.