# How do i find the probability of this>?

1. Nov 13, 2009

### Dell

How do i find the probability of this>?
in my closet i have 10 paris of shoes, i randomly take out 8 shoes,
what is the probability that i will take out exactly one pair?

how do i solve this??

2. Nov 13, 2009

### redargon

this sounds like a homework question. post it in the HW section and follow the guidelines!

3. Nov 13, 2009

### clamtrox

If you own 10 pairs of shoes, you could always try a Monte Carlo-approach. :-)

If you pick out one shoe, what are the odds that the next shoe I pick is gonna give me a pair? If that doesn't work, how about the next one?

4. Nov 13, 2009

### Geekchick

Try rewriting the problem ie. Look at it as having 2 red, 2 blue, 2 yellow, 2 green, 2 purple, 2 orange, 2 violet, 2 pink, 2 black, and 2 white balls. Then given the twenty balls you are trying to make lines of eight without replacement. Thus the probability you're looking for is the probability that you will draw exactly two of one color and one of six other colors.

5. Nov 14, 2009

### Dell

i looked at it like this, what is the chance i can pick 7 different(non paris) shoes, and thae last one being the pair of one of them

for the 1st i have 20 options,
for the second i have 18, ( 20 minus the 1 i picked, minus its partner)
for the second 16
...
for the seventh 8
for the eighth i have 7 options( the partner of any of the previous 7)

so i have 20*18*16*14*12*10*8*7 ways of choosing exactly one pair

P(one pair)=20*18*16*14*12*10*8*7/20P8=0.10669

is this possible?

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