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?
A). StartFraction 7 C 2 Over 12 C 2 EndFraction
B). StartFraction 7 P 2 Over 12 P 2 EndFraction
C). StartFraction (3 C 1) (4 C 1) Over 12 C 2 EndFraction
D). StartFraction (3 P 1) (4 P 1) Over 12 P 2 EndFraction
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Answers
Given : At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives.
To find : probability that a student chooses an art elective and a history elective
Step-by-step explanation:
Art electives = 3
History electives = 4
Computer Electives = 5
Total Electives = 3 + 4 + 5 = 12
Each student can choose two electives.
Two electives our of 12 can be selected in ¹²C₂ ways
a student chooses an art elective and a history elective
= ³C₁ * ⁴C₁
probability that a student chooses an art elective and a history elective
= (³C₁ * ⁴C₁ ) / ¹²C₂
option C is correct
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