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?

ant101
Feb 19, 2018

#1**0 **

I'll try , Ant!

Say your fist pick is

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)

ElectricPavlov
Feb 19, 2018

#3**0 **

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**0 **

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!

tertre
Feb 19, 2018

#5**0 **

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