(a) Among the strictly increasing sequences of integers that start with 1 and end with 7 are:
(i) 1, 7
(ii) 1, 3, 4, 7
(iii) 1, 2, 4, 5, 6, 7
How many such strictly increasing sequences of integers start with 1 and end with 7?
(b) How many strictly increasing sequences of integers start with 3 and end with 9?
(c) How many strictly increasing sequences of integers start with 1 and end with 37? How many start with 62 and end with 98?
(d) Generalize the results in parts (a) through (c).