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?
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I think the answer is B<==

Answer 1

Permutation helps us to know the number of ways an object can be arranged in a particular manner. The correct option is B.

What are Permutation and Combination?

Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

$^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}$

where,

n is the number of choices available,

r is the choices to be made.

The probability that both students have chosen are sophomores is,

(6/20) × (5/19) = 30/380

Similarly, The expression that represents the probability that both students have chosen are sophomores is,

(⁶P₁ × ⁵P₁)/(²⁰P₂) = 30/380

Hence, the correct option is B.

Learn more about Permutation and Combination:

https://brainly.com/question/11732255

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