selections problem, please help me understand

[lorelondon2013]

Hi

I came across the following problem on some other forum and I feel stuck on how to solve it myself. Here it is:

A box contains a total of 30 balls out of which 6 are yellow, 7 are green, 8 purple and 9 blue.
a) what would be the total no. of selections necessary to ensure that 2 balls of the same colour are chosen?
b) what would be the total no. of selections necessary to ensure that 2 balls of different colour are chosen?

Personally I've got a) 5 and b) 10. But I am not sure.
Can anyone shed light on this?

thanks

[tommywallach]

Hey Lore,

You did it totally right! There's no trick to this; you just have to think about it.

For (A), if we've picked 5 balls, we must have at least two of the same color, because once we've picked one yellow, one green, one purple, and one blue, we must now pick a duplicate.

For (B), we could conceivably pick all 9 of the blue balls, but then our 10th pick would have to be a different color.

Perfect!

-t

[lorelondon2013]

great! I'm glad I got it right :) thanks!

[tommywallach]

Glad to help!

-t