Question

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?
a $\frac{1}{20}$
b $\frac{1}{10}$
c $\frac{1}{8}$
d $\frac{1}{7}$
e $\frac{1}{4}$

Explanation:

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

Use the combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 5\) and \(r=2\).

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Step2: Calculate the number of favorable cases

There is only 1 way to select Adam and Ella.

Step3: Calculate the probability

Probability \(P=\frac{\text{Number of favorable cases}}{\text{Total number of cases}}\). So \(P=\frac{1}{10}\)

Answer:

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