John, Cal, and Mark share an apartment, and a list is made showing who is supposed to wash dishes for each day from Monday through Friday

number of possible outcomes???And how do you get the answer?

3/27/2006 8:40:00 PM

Let's start with this: If there are 3 people, and 3 days, the first day there are 3 possibilities, day 2 there are 2 possibilities, and day 3 there is one possibility (assuming no one washes dishes twice in 3 days). In 5 day, assuming no one washes dishes more than twice in 5 days and there are no restrictions like if John washes on Monday he can't wash on Tuesday, there would be 3x3x2x2x1 possibilities. It gets more complex if you start adding contingencies.

3/27/2006 8:47:09 PM

Stop trying to get out of your chores and wash the damned dishes.

3/27/2006 8:54:33 PM

Damn..I'm lost.

So if there are 3 ppl and 5 days..can I say

that there are 3 possibilities for Day 1

Day 2: there are still 3 possibilities right..because there are no restrictions..and at least two of those days that week..someone will be washing again.

Damn. I know this is simple but I just can't get it.

3/27/2006 8:55:40 PM

oh no. I get it.

Monday-3 outcomes
tuesday-3
wed-3
thurs-3
fri-3

3x3x3x3x3=243

thanks..you helped a lot.

3/27/2006 9:07:50 PM

Quote :

"In 5 day, assuming no one washes dishes more than twice in 5 days and there are no restrictions like if John washes on Monday he can't wash on Tuesday, there would be 3x3x2x2x1 possibilities."

Actually it's a bit more complicated than that. Your answer gives 36.

You have to pick which of the 3 only washes one day, so 3 choose 1 = 3.

Multiply this by 5 choose 1 = 5, to pick the one day this person washes.

Then you have 4 chooes 2 = 6 ways to give two of the four days to the next person.

The third guy takes what's left over.

3 x 5 x 6 = 90.

3/28/2006 6:43:02 PM

Another way to do that would be to take 243 total possibilities.

Subtract off the ways someone could do all 5 days, pick one of the 3 people: AAAAA = 3 choose 1 = 3.

Subtract ways someone could do four, pick which of the 3 people, which 4 days, then pick one of the other two people for the fifth day: AAAAB = 3*5*2 = 30.

Then something like AAABB 3*10*2 = 60 ways,

AAABC = 60 ways

243 - 3 - 30 - 60 - 60 = 90.

3/28/2006 6:48:08 PM