Question

Shaun is planting trees along his driveway, and he has 66 redwoods and 66 pine trees to plant in one row. What is the probability that he randomly plants the trees so that all 66 redwoods are next to each other and all 66 pine trees are next to each other

Answer 1

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

Explanation:

The trees are arranged, so the arrangements formula is used to solve this question. Also, a probability is the number of desired outcomes divided by the number of total outcomes.

Arrangements formula:

The number of possible arrangements of n elements is given by:

`A_n = n!`

Desired outcomes:

Two cases:

6 redwoods(6! ways) then the 6 pine trees(6! ways)

6 pine trees(6! ways) then the 6 redwoods(6! ways)

So

`D = 2*6!*6!`

Total outcomes:

12 trees, so:

`D = 12!`

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

`p = (D)/(T) = (2*6!*6!)/(12!) = 0.0022`

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