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?

StartFraction 7 C 2 Over 12 C 2 EndFraction
StartFraction 7 P 2 Over 12 P 2 EndFraction
StartFraction (3 C 1) (4 C 1) Over 12 C 2 EndFraction
StartFraction (3 P 1) (4 P 1) Over 12 P 2 EndFraction

(3C1 × 4C1)/12C2

Step-by-step explanation:

Total electives = 3 + 4 + 5 = 12

Art: 3C1

History: 4C1

1 Art & 1 History = 3C1 × 4C1

Probability = (3C1 × 4C1)/12C2

Step-by-step explanation:

Since it doesn't matter whether you choose Art first or History first - order doesn't matter so it is a COMBINATION (C)

(if order mattered, you would use Permutation (P))

Since you are choosing Art AND History, you multiply them

(OR would be addition, instead of multiplication)

Since you are looking for probability, you need to divide by the total number of combinations.

3 Art electives choose 1 = ₃C₁

4 History electives choose 1 = ₄C₁

12 Total electives choose 2 = ₁₂C₂

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values