Answer to Question #142562 in Algebra for Eugene Keator

Question

If 6 science fair exhibits are chosen at random from 4 biology, 7 chemistry, and 9 physics exhibits to

go to the county finals, what is the probability that there will be 2 from each subject area?

Answer 1

Biology = 4

Chemistry = 7

Physics = 9

Total = 20

Number of ways of choosing 6 science fair exhibit out of 20 = ²⁰C₆ = 38760

Number of ways of choosing 2 biology = ⁴C₂ = 6

Number of ways of choosing 2 chemistry = ⁷C₂ = 21

Number of ways of choosing 2 physics = ⁹C₂ = 36

Total number of ways of choosing 2 each of Biology, chemistry and physics = 6 × 21 × 36 = 4536

Probability of choosing 2 each of Biology, chemistry and physics = $\frac{4536}{38760}$ = 0.1170