Eight women of eight different heights are to pose for a photo in two rows of four. Each woman in the second row must stand directly behind a shorter woman in the first row. In addition, all of the women in each row must be arranged in order of increasing height from left to right. Assuming that these restrictions are fully adhered to, in how many different ways can the women pose?
(A) 2
(B) 14
(C) 15
(D) 16
(E) 18
(B) 14
(C) 15
(D) 16
(E) 18
There are too many conditions to use a forumla straight away, so let’s work out some options manually. I generally use this approach where a lot of conditions appear in a GMAT question.
Shortest (1) and highest (8) women are fixed:
XXX8
1XXX
XXX8
1XXX
2 and 7 have two options, so total 4 patterns:
1:
2xx8
1xx7
|2468| |2568|
|1357| |1347|
|1357| |1347|
2.
2x78
1xxx
|2478| |2578| |2678|
|1356| |1346| |1345|
|1356| |1346| |1345|
3.
xxx8
12x7
|4568| |3468| |3568|
|1237| |1257| |1247|
|1237| |1257| |1247|
4.
xx78
12xx
|3478| |3678| |3578| |5678| |4578| |4678|
|1256| |1245| |1246| |1234| |1236| |1235|
|1256| |1245| |1246| |1234| |1236| |1235|
14 options.
B
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