[求助]Two math problems

jtcjxk

1. A gardener is going to plant 2 red rosebushes and 2 white. Select ramdomly, one at a time and plant them in a row. What is the probability that the 2 in the middle will be red?

Answer: 1/6 (I listed all the situations. but how to get this result by "calculation"?)

2. A photographer will arrange 6 people of 6 different heights for photograph by placing them in 2 rows of three so that each person in the first row 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 teh person standing in front of him/her. How many such arrangements of the 6 people are possible?

Answer: 5 (I have no idea how to get this)

Thanks

inizhangyang

1. 两个红的在中间，他们可以相互调换，就是P22，另外两个白的在两边，这定了，也可以互换位置，也是P22 。整个的排列就是4个随便排，就是P44，所以结果是P22*P22/P44=1/6

2. 这道题用列举法，很简单，把6个人变成号，123456，这也是他们的高度，左高于右，前大于后，因此最大的数6只能排在第2排最左边。

6 x x   那么5 只能排在2个位置 就是 6 5 x 或  6 x x    然后分类再讨论4

x x x                              x x x      5 x x

最后5种结果是 6 4 2    6 4 3    6 5 2     6 5 3    6 5 4     

              5 3 1    5 2 1    4 3 1     4 2 1    3 2 1