Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. which expression represents the pro

Question

2 years ago

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Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. which expression represents the pro

bability that both students chosen are sophomores? startfraction (20 c 6) (19 c 5) over 20 c 2 endfraction startfraction (20 p 6) (19 p 5) over 20 p 2 endfraction

Mathematics

1 answer:

schepotkina [342] · Answer 1 · 2023-10-11T09:55:06+03:00

The probability expression is $\frac{^{6}C_2}{^{20}C_2}$

<h3>How to determine the probability expression?</h3>

The given parameters are

Sophomore = 6
Freshmen = 14

The total number of people is

n = 20

2 of the 20 people are to be selected.

So, the number of selection is

$n = ^nC_r$

This gives

$n = ^{20}C_2$

The expression that represents both students being sophomore is

$n = ^{6}C_2$ --- i.e. 2 students selected from 6

The probability is then represented as:

$\frac{^{6}C_2}{^{20}C_2}$

Hence, the probability expression is $\frac{^{6}C_2}{^{20}C_2}$