19) A six-sided die is rolled twelve times. What is the probability that the die will show an even number exactly nine times? 20) A gambler places a bet on a horse race. To win, she must pick the top...

Find the probability of each event.

Extracted text: 19) A six-sided die is rolled twelve times. What is the probability that the die will show an even number exactly nine times? 20) A gambler places a bet on a horse race. To win, she must pick the top three finishers in order. Seven horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win her bet?