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stepladder [879]
3 years ago
7

Gretchen has eight socks, two of each color: magenta, cyan, black, and white. she randomly draws four socks. what is the probabi

lity that she has exactly one pair of socks with the same color?
Mathematics
1 answer:
Svetllana [295]3 years ago
3 0
Begin by computing the number of all the possibilities:
It is given by the following formula:C_8^4=\frac{8!}{4!(8-4)!}= \frac{8\times7\times6\times5}{4\times3\times2}=70
Computing the number of favorable cases:
Exactly one pair of socks with the same color means either one magenta pair, 
or one cyan pair, or one black pair or one white pair:
Number of possibilities with one magenta pair means"a magenta pair plus two socks with different colors from three possibilities" means 3 possibilities. 
Same computation for the other colors. 
Adding we get: 3+3+3+3=12\text{ possibilities }
By definition, the probability of an event is the number of favorable cases over the number of possible cases:
\frac{12}{70}= \frac{6}{35}

The probability is \frac{6}{35}
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