Question

Bianca is planting trees along her driveway, and she has 55 sycamores and 55 palm trees to plant in one row. What is the probability that she randomly plants the trees so that all 55 sycamores are next to each other and all 55 palm trees are next to each other

Answer 1

Answer:

0.0079 = 0.79% probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other.

Step-by-step explanation:

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

The trees are arranged, so, to find the number of outcomes, the arrangements formula is used.

Arrangements formula:

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

$A_n = n!$

Desired outcomes:

5 sycamores(5! possible ways) and then the 5 palm trees(5! possible ways)

5 palm trees(5! possible ways) then the 5 sycamores(5! possible ways).

$D = 2*5!*5!$

Total outcomes:

Arrangements of 10 plants, so:

$T = 10!$

What is the probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other?

$p = \frac{D}{T} = \frac{2*5!*5!}{10!} = 0.0079$

0.0079 = 0.79% probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other.