SOLUTION: There are 12 different colored PAIRS (24 socks total, 12 different colors) of socks in a drawer. If a person takes 10 socks from that drawer, what is the probability that none of t

Algebra ->  Permutations -> SOLUTION: There are 12 different colored PAIRS (24 socks total, 12 different colors) of socks in a drawer. If a person takes 10 socks from that drawer, what is the probability that none of t      Log On


   

Question 926855: There are 12 different colored PAIRS (24 socks total, 12 different colors) of socks in a drawer. If a person takes 10 socks from that drawer, what is the probability that none of these socks are pairs?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
There are 12 different colored PAIRS (24 socks total, 12 different colors) of socks in a drawer. If a person takes 10 socks from that drawer, what is the probability that none of these socks are pairs? 
That means we have to take out 10 socks of 10 different colors.

We can choose 10 different colors in C(12,10) = 66 ways.

We can choose the sock of each of the 10 colors in 2 ways each.
So that's 2%5E10=1024 ways to choose the socks that go with the ten colors.

So the numerator of the probability is 66*1024 = 67584 ways. 

The denominator is C(24,10) = 1961256.

So the probability is  67584%2F1961256=256%2F7429

or as a decimal 
0.03445955041055323731323192892717727823394804145914658769686364248216449051016287521873738053573832278906986135415264503...

Edwin