TOUGH GUY wrote:

A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?

A 5

B 6

C 9

D 24

E 26

Interesting question:

Assuming the height of each person = 1, 2, 3, 4,5, 6 (it's irrational but the number makes it easy to compare)

From the question, we can conclude that 1 must be on the lower left and 6 must be the upper right. So 2 position are fixed.

Case 1: The most common arrangement.

4_5_6 <--- row 2

1_2_3 <--- row 1

Case 2: Bring 5 down and bring 3 up

3_4_6

1_2_5

Case 3: Bring 5 down and bring 2 up

2_4_6

1_3_5

Case 4: Bring 4 down and bring 3 up

3_5_6

1_2_4

Case 5: Bring 4 down and bring 2 up

2_5_6

1_3_4

5 cases total. The answer is A?