Mr. Flowers plants ten rosebushes in a row. Eight of the bushes are white and two are red, and he
plants them in random order. What is the probability that he will consecutively plant seven or more
The Attempt at a Solution
correct set up for the answer is 9/ 10 choose 2
There are 9 ways to plant the rose bushes with 7 or more white in a row.
7w w r r
7w r w r
7w r r w
r r 7w w
w r 7w r
r w 7w r
r r w 7w
r w r 7w
w r r 7w
At first, I thought the answer will be 9/10!, since there are 9 different possible combinations where there are at least 7 whites in a row, and of the 10 rose bushes, there are 10! ways to shift move them around.
I know the answer is to divide 10 choose 2 red bushes by 9, but I dont know why.