+0

# Quick problem, need a solution or just some help!

+1
599
2
+444

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
+97498
+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

Dec 9, 2017
#2
+444
+3

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

Mr.Owl  Dec 10, 2017