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?

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

Answer 1

Answer:   $\bold{\dfrac{(_3C_1)(_4C_1)}{_{12}C_2}}$

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

                                  $\text{Probability}=\dfrac{(_3C_1)(_4C_1)}{_{12}C_2}$

Answer 2

Answer:

(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