Let A be a sequence of 8 distinct integers sorted in ascending order. How many…

To form sequences B and C from the sorted sequence A of 8 distinct integers, we need to choose 5 elements for B and the remaining 3 for C. Since both sequences must be in ascending order and merging them gives back A, the relative order of elements is preserved. This means we are simply choosing 5 positions out of 8 for B (the rest go to C). The number of ways to do this is given by the binomial coefficient C(8,5), which equals 56. Therefore, there are 56 distinct pairs of sequences (B,C) that satisfy the conditions.