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Charity is planting trees along her driveway, and she has 6 pine trees and 6 willows to plant in one row. What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other

User Frayt
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1 Answer

4 votes

Answer:

0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the elements are arranged, so we have to use the arrangements formula.

Arrangements formula:

The number of possible arrangements of n elements is:


A_(n) = n!

Desired outcomes:

Pine trees(6!) then the willows(6!) or

Willows(6!) then the pine trees(6!). So


D = 2*6!*6! = 1036800

Total outcomes:

12 trees, so:


T = 12! = 479001600

What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other?


p = (D)/(T) = (1036800 )/(479001600 ) = 0.0022

0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.

User Shu
by
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