If I only pic 2 lottery balls?!?

In the lottery, 6 balls numbered 1 to 59 are drawn from a machine (lets exclude the bonus ball for the purpose of this question).

Now, lets say instead of choosing 6 balls (like you normally do) you only get to choose 2.

What then are the odds that both these balls will show up within the 6 balls which are randomly drawn from the machine?



Extra question... What is the chance of this happening 3 times in a row?

Thanks

What are your thoughts? What have you tried? Please share with us any and all work you've done on this problem, even if you know it's wrong. Thank you.