We use binary trees to analyze two algorithms, insertion sort and multiple quckselect. In each case, we consider the number of comparisons consumed as a measure of performance. We assume that the ranks of the n data values being searched or sorted form a random permutation of the integers {l,...,n}. For insertion sort, we consider the limiting distribution of the number of comparisons consumed in the process of sorting the n keys. We present an average-case analysis of the number of comparisons multiple qukkselect (MQS) requires for simultaneously finding several order statistics in the data set.