Bullzi wrote:Hello..
I know this is an old post, still, I had a question I wanted some help with. So, my first instinct on reading this problem was to start with multiplying the 12 with 9 * 8
Now, the only reason this approach isn't right is that the selection of 2 from 9 inexperienced astronauts isn't unique and hence doesn't qualify for the fundamental counting principle to be used?
Thanks
Bullzi
You're right - the only issue here is that you're doing a PERMUTATION (in which order matters) rather than a COMBINATION (in which order does).
For instance, suppose we have four people and we're picking two. By your logic, we'd have 4 * 3 options, but if we list them out, we see
AB
BA
AC
CA
AD
DA
BC
CB
BD
DB
CD
DC
Notice how we've overcounted? (This is a very easy mistake to make, by the way: I still make it myself sometimes, despite teaching these basic combo problems for five years!)
So we have to cut out the duplicates, and divide by 2. We divide by 2 here because we don't want to arrange our 2 people, so we divide by the number of ways that 2 people can be arranged.
