Probability

[pure1978]

Ok we spent like literally 1 day on permutaions and combinations and I'm not really clear on it and I'm hoping someone can help me see the exact process that is going on when there is the combination of the 2 in the same problem. An example would be say there are 6 black socks, 4 blue socks, and 7 brown socks in a drawer, what is the probability that you will pull out 2 of the same color (without looking of course).

Here is how I have tried solving it but I am unsure if this is correct.

C(6,2) +C(4,2) +C(7,2) =

15 + 6 + 21 = 42/P(17,2) =

42/272 = 15.4% chance

is this correct and if not what is the correct procedure to follow.

 

[arthur ohlsten]

with 6 black socks,4 blue, and 7 brown
what is the probability of choosing 2 black OR 2 bl;ue OR 2 brown socks?

when you say OR you add, when you say AND you multiply
P=[C6,2 + C4,2 + C7,2] / C17,2
P=[15+6+21] / [136]
P=42/136 answer your denominator is in error I believe
P=21/68 answer
P=.31 answer

please check math.
Arthur

 

[Denis]

Another "way":

blue : 4/17 * 3/16 = 12/272
black:6/17 * 5/16 = 30/272
brown:7/17 * 6/16= 42/272

12/272 + 30/272 + 42/272 = 84/272 = 21/68 (as per Arthur)