Silly Socks: Solution

Thanks for visiting NZMaths.
We are preparing to close this site by the end of August 2024. Maths content is still being migrated onto Tāhūrangi, and we will be progressively making enhancements to Tāhūrangi to improve the findability and presentation of content.
 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Alex doesn’t mind what socks he puts on in the morning. He has a pair of red socks and a pair of blue socks.  Each morning he just takes out the first two socks he finds. So some mornings he wears a pair of red socks and some mornings he wears a pair of blue socks. But some mornings he wears a ‘silly pair’ consisting of one red and one blue sock.

If he gets a pair of green socks as well, how many different pairs of socks, silly and otherwise, can he wear?
 
Solution
 
Alex can make up six pairs of socks altogether. 
 
If we make a list we find:
  1. red, red
  2. red, blue
  3. red, green
  4. blue, blue
  5. blue, green
  6. green, green
Extension
 
How many different pairs of socks, silly and otherwise, could Alex wear if he had six normal pairs of socks that were red, blue, green, white, black, and yellow?
 
What if he had 100 differently coloured socks?