Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. Which expression represents the probability that both students chosen are sophomores?

Answer: [tex]\frac{6_C_2}{20_C_2}[/tex]Step-by-step explanation:According to the question total sophomores = 6Total freshmen = 14Therefore, total persons = 6+ 14 = 20Thus, If two person are chosen the probability that both are sophomores,P =  Total combination of 2 person from the group of 6 sophomores/ total personsP = [tex]\frac{6_C_2}{20_C_2}[/tex], which is the required expression.Note: we can further solve the value of P as follow,⇒P= [tex]\frac{6!/4!2!}{20!/18!2!}[/tex]⇒P=[tex]\frac{30/2}{10\times 19}[/tex]⇒P=[tex]\frac{15}{190}[/tex]