Suppose we have a machine with three instruction types, which we'll call A, B, and C. All instructions require one clock tick, and the machine can execute one instruction of each type at each clock....

Suppose we have a machine with three instruction types, which we'll call A, B, and C. All instructions require one clock tick, and the machine can execute one instruction of each type at each clock. Suppose a loop consists of six instructions, two of each type. Then it is possible to execute the loop in a software pipeline with an initiation interval of two. However, some sequences of the six instructions require insertion of one delay, and some require insertion of two delays. Of the 90 possible sequences of two A's, two B's and two C's, how many require no delay? How many require one delay?

Hint: There is symmetry among the three instruction types so two sequences that can be transformed into one another by permuting the names A, B, and C must require the same number of delays. For example, ABBCAC must be the same as BCCABA.