There are b4 (= 14) ways to arrange 1, 2, 3, . . . , 8 in two rows of four so that (1) the integers increase in value as each row is read, from left to right, and (2) in any column the smaller integer is on top. Find, as in part (d) of Example 1.43,
(a) The arrangements that correspond to each of the following.
(i) 10110010
(ii) 11001010
(iii) 11101000
(b) The lists of four l's and four 0's that correspond to each of these arrangements of 1, 2, 3, ... , 8.
(i) 1 3 4 5
2 6 7 8
(ii) 1 2 3 7
4 5 6 8
(iii) 1 2 4 5
3 6 7 8