Hello, I would like some help in solving these problems. Please explain how you arrived at your answer if you don't mind.
1. Ten finalists are competing in a race at the Canada games:
a) In how many different orders can the competitors finish the race?
b) How many ways could the gold, silver, and bronze medal be awarded?
c) One of the finalists is a friend from your town. How many of the possible finishes would include them winning a medal?
d) How many possible finishes would leave your friend out of the medal standings?
e) Suppose one of the competitors is injured and cannot finish the race. How does that affect your previous answers?
f) How would the competitor's injury affect your friend's chances of winning a medal? Explain your reasoning. What assumptions have you made?
I understand that this is not a homework service. I have tried the questions, but I am not sure if they're right. I just wanted to confirm by comparing answers.
21a) 10! = 10x9x8x7x6x5....x2x1= 3628800
b) 10x9x8= 720 since there are only 3 positions to fill
c) 9x8x3=216
d) 9x8x7 =504
e) I'm not sure
f) I'm not sure
I'm also having problems explaining HOW I arrived to these answers. I'm just doing it because that's how I was taught to. I don't know how to 'justify' them.