Question

At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives.

Which expression represents the probability that a student chooses an art elective and a history elective?

Answer 1

the correct answer is C

Step-by-step explanation:

Answer 2

Ans: Correct Option is (C) => P =
`( (3C_1)(4C_1))/(12C_2)`

Step-by-step explanation:
According to the definition of probability:
Probability of an Event = (Number of favorable outcomes) / (Total number of possible outcomes or sample space)

or,

P = O / S;

First let us find Total number of Possible Outcomes(S):

`S = (3+4+5)C_2` = 12
`C_2` (Since a student can choose two electives)

In mathematical terms, you can read S as:"The sample space is equals to the combination of 12 taken 2."

Number of favourable outcomes(O):
O = (3-art-electives)
`C_1` * (4-history-electives)
`C_1`
O = (3
`C_1`)(4
`C_1`)

In mathematical terms, you can read O as:"The outcome is equal to combination of 3 taken 1 times combination of 4 taken 1."

Hence,
Probability P = O/S
P =
`( (3C_1)(4C_1))/(12C_2)`