# Thread: Tree/Permutation - Urn problem

1. ## Tree/Permutation - Urn problem

An urn contain one white, two red, and two blue marbles. A game is played by selecting marbles until the white one is selected. How many outcomes does this game have?

I got 65, but apparently it's wrong.

My reasoning, Red had 16 outcomes.

16 (red 1)+16 (red 2)+16 (blue 1)+16 (blue 2) +1 (white)=65

2. Originally Posted by Sakurazaki
An urn contain one white, two red, and two blue marbles. A game is played by selecting marbles until the white one is selected. How many outcomes does this game have?
This is an absolutely poorly worded problem. There are two readings.
If we select a ball and then discard it, then there are at most six ways for this to be done.

If we select a ball and then return it, then there are infinitely many ways this to be done.
There is no reason that a white ball is ever selected.

3. It is we select a ball and then discard it. But I tried inputing six and it still says it's wrong.

4. Hello Sakurazaki
Originally Posted by Sakurazaki
An urn contain one white, two red, and two blue marbles. A game is played by selecting marbles until the white one is selected. How many outcomes does this game have?

I got 65, but apparently it's wrong.

My reasoning, Red had 16 outcomes.

16 (red 1)+16 (red 2)+16 (blue 1)+16 (blue 2) +1 (white)=65
It doesn't take long to list all the possibilities. Here they are:

W
RW
BW
RRW
RBW
BRW
BBW
RRBW
RBRW
BRRW
RBBW
BRBW
BBRW
RRBBW
RBRBW
RBBRW
BRRBW
BRBRW
BBRRW

So I reckon the answer is 19