Question

Organized Counting Problem:

1. Ten finalists are competing in a race at the Canada games:
a) In how many different orders can the competitors finish the race?
\(10\ \times\ 9\ \times\ 8 ......\times\ 1=3628800\)
b) How many ways could the gold, silver, and bronze medal be awarded?
\(10\ \times\ 9\ \times\ 8=720\)
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?

I need help with letter C.

Answer 1

she could be first, then \(9\times 8\) or second \(9\times 8\) or third \(9\times 8\) so i believe the answer is
\[3\times 9\times 8\]

Answer 2

but i suck at these so get a second opinion

Answer 3

why 3 though? what i mean is, should it be \(9 \times 8 \times 7\)?
but i'm not sure though
i'm really confused

Answer 4

last one you got \(9\times 8\times 7\) right?

Answer 5

three represents the 3 positions your friend could end up in
first, second or third

Answer 6

if she comes in first, then second has 9 choices and third has 8
if she comes is second, then first has 9 choices and third has 8
if she comes in third, then first has 9 choices, second has 8

Answer 7

so
\[3\times 9\times 8\]

Answer 8

aah okay i get it. thanks! ^_^

Answer 9

yw