Question

Let A be a sequence of 8 distinct integers sorted in ascending order. How many distinct pairs of sequences, B and C are there such that (i) each is sorted in ascending order, (ii) B has 5 and C has 3 elements, and (iii) the result of merging B and C gives A ?

• A. 2
• B. 30
• C. 56
• D. 256

Answer 1

The correct option is C 56

This corresponds to an ordered partition of 8 elements into two groups, the first with 5 elements and second with 3 elements. The number of ways of doing this is
$P(8;5;3)=\frac{8!}{5!3!}=56$