Question

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 1

The probability that both the chosen students are sophomores is 6/20 or 3/10 simplified.
the expresión that represents the probability that both students have chosen are sophomore is (6c1) (5c1) /(20c2) 

Answer 2

Answer: $\frac{6_C_2}{20_C_2}$

Step-by-step explanation:

According to the question total sophomores = 6

Total freshmen = 14

Therefore, total persons = 6+ 14 = 20

Thus, If two person are chosen the probability that both are sophomores,

P =  Total combination of 2 person from the group of 6 sophomores/ total persons

P = $\frac{6_C_2}{20_C_2}$, which is the required expression.

Note: we can further solve the value of P as follow,

⇒P= $\frac{6!/4!2!}{20!/18!2!}$

⇒P=$\frac{30/2}{10\times 19}$

⇒P=$\frac{15}{190}$