a middle school chess club has 5 members: adam, bradley, carol, dave, and ella. two students from the club…

a middle school chess club has 5 members: adam, bradley, carol, dave, and ella. two students from the club will be selected at random to participate in the county chess tournament. what is the probability that adam and ella will be selected?\na $\frac{1}{20}$\nb $\frac{1}{10}$\nc $\frac{1}{8}$\nd $\frac{1}{7}$\ne $\frac{1}{4}$

a middle school chess club has 5 members: adam, bradley, carol, dave, and ella. two students from the club will be selected at random to participate in the county chess tournament. what is the probability that adam and ella will be selected?\na $\frac{1}{20}$\nb $\frac{1}{10}$\nc $\frac{1}{8}$\nd $\frac{1}{7}$\ne $\frac{1}{4}$

Answer

Explanation:

Step1: Calculate the total number of ways to select 2 students from 5

Use the combination formula (C(n,k)=\frac{n!}{k!(n - k)!}), where (n = 5) and (k=2). [ \begin{align*} C(5,2)&=\frac{5!}{2!(5 - 2)!}\ &=\frac{5!}{2!×3!}\ &=\frac{5\times4\times3!}{2\times1\times3!}\ &=10 \end{align*} ]

Step2: Calculate the number of ways to select Adam and Ella

There is only (1) way to select Adam and Ella.

Step3: Calculate the probability

Probability (P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}). The number of favorable outcomes is (1) (selecting Adam and Ella), and the total number of outcomes is (10). So (P=\frac{1}{10})

Answer:

B. (\frac{1}{10})