Chris wants to put six plants in a row on his windowsill. He randomly chooses each plant to be an aloe plant, a basil plant, or a violet. What is the probability that either exactly four of the plants are aloe plants or exactly five of the plants are basil plants?

Mr.Owl Dec 9, 2017

#1**+4 **

Hi Mr Owl,

Chris wants to put six plants in a row on his windowsill. He randomly chooses each plant to be an aloe plant, a basil plant, or a violet. What is the probability that either exactly four of the plants are aloe plants or exactly five of the plants are basil plants?

The number of ways that the 6 plants can be arrangesd is 3^6 = 729

The number of ways that the first 4 plants are aloe vera and the last 2 are not is 1*1*1*1*2*2 = 4

**The number of ways that exactly 4 plants are aloe vera is 6C4*4 = 15*4 = 60**

The number of ways that the first 5 plants are basil 1*1*1*1*1*2 = 2

**The number of ways that the first 5 plants are basil 6C5*2 = 6*2=12**

There are no overlaps with these **so**

The probabity you want is (60+12) / 729 = 72/729 = 8/81

Melody Dec 9, 2017