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# help...combinations

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I have 10 distinguishable socks in my drawer: 4 white, 4 brown, and 2 blue. In how many ways can I choose a pair of socks, provided that I get two socks of the same color?

Feb 19, 2018

#1
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I'll try , Ant!

white       then there are 3 choices w    4 choices br     2 choices bl

First pick is

brown    then there are 4 choices w    3 choices br    2 choices bl

First pick is

blue      then there are  4 choices w   4 choices br     1 choice bl

Add the red choices up....looks like 7 ways to get a pair of mathcing socks !

(I do not promise this is correct , Ant.....just my best try)

Feb 19, 2018
edited by ElectricPavlov  Feb 19, 2018
#2
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You're close, EP!

tertre  Feb 19, 2018
#3
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Haha!   HOW close???     I told Ant offline I was not very good at these type Q's, but I would try!

ElectricPavlov  Feb 19, 2018
#4
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The socks must be either both white, both brown, or both blue. If the socks are white, there are \(\binom{4}{2} = 6\) choices. If the socks are brown, there are \(\binom{4}{2} = 6\) choices. If the socks are blue, there is \(\binom{2}{2} = 1\) choice. So the total number of choices for socks is \(6+6+1=\boxed{13}\).         6 away, EP!

Feb 19, 2018
#5
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I think I'm slowly getting it.....  you are choosing a PAIR at a time (Which I think, is actually what the question is asking)..I am selecting one sock at a time in my answer....

ElectricPavlov  Feb 19, 2018
#6
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Yes, that's correct.

tertre  Feb 19, 2018