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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?

 Dec 9, 2017
 #1
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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

 Dec 9, 2017
 #2
avatar+470 
+4

Thanks! 8/81 Was the right answer! Thanks a bunch!

Mr.Owl  Dec 10, 2017

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