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

Explanation:

Step1: Calculate total number of ways to choose 2 trees

Use combination formula (C(n,r)=\frac{n!}{r!(n - r)!}), where (n = 5), (r=2). [ \begin{align*} C(5,2)&=\frac{5!}{2!(5 - 2)!}\ &=\frac{5\times4\times3!}{2\times1\times3!}\ &=10 \end{align*} ]

Step2: Calculate number of ways to choose 1 deciduous and 1 evergreen tree

Number of ways to choose 1 deciduous tree ((n_1)): (C(3,1)=\frac{3!}{1!(3 - 1)!}=\frac{3\times2!}{1\times2!}=3) Number of ways to choose 1 evergreen tree ((n_2)): (C(2,1)=\frac{2!}{1!(2 - 1)!}=\frac{2\times1!}{1\times1!}=2) By multiplication principle, number of ways to choose 1 deciduous and 1 evergreen tree (n=n_1\times n_2=3\times2 = 6)

Step3: Calculate probability

Probability (P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{6}{10}=0.6) Convert to percentage: (0.6\times100% = 60%)

Answer:

60%