a landscaper is selecting two trees to plant. he has five to choose from. three of the five are deciduous…

Explanation:

Step1: Calculate total combinations

The number of ways to choose 2 trees out of 5 is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 5$ and $r=2$. So $C(5,2)=\frac{5!}{2!(5 - 2)!}=\frac{5\times4}{2\times1}=10$.

Step2: Calculate favorable combinations

The number of ways to choose one deciduous tree out of 3 and one ever - green tree out of 2 is the product of the number of ways to choose each type. Using the combination formula, the number of ways to choose 1 deciduous tree out of 3 is $C(3,1)=\frac{3!}{1!(3 - 1)!}=3$, and the number of ways to choose 1 ever - green tree out of 2 is $C(2,1)=\frac{2!}{1!(2 - 1)!}=2$. The number of favorable combinations is $C(3,1)\times C(2,1)=3\times2 = 6$.

Step3: Calculate probability

The probability $P$ is the number of favorable combinations divided by the total number of combinations. So $P=\frac{6}{10}=0.6$.

Answer:

60%