There are 15 yellow ball , 10 blue balls and 8 green balls mixed up in a bag. Paul takes out at least 2 balls of each colour randomly what is the least number of balls need to take out from bag

Question

Could you please send me the answer as soon as possible

 

Thanks

Answer 1

I read this as: what is the minimum number of balls that must be drawn to guarantee at least two balls of each colour.

If so:

If he draws 15 balls, by chance he could pick all the yellow balls but no blue or green. So he must draw more than 15.

If he draws 25 balls, by chance he could pick all the yellow and blue balls but no green. So he must draw more than 25.

To ensure at least two greens, he should draw 27. All 28 possible outcomes would be:

(yellow,blue,green)=

(15,10,2), (15,9,3), ..., (15,4,8),

(14,10,3), (14,9,4), ..., (14,5,8),

(13,10,4), (13,9,5), ..., (13,6,8),

(12,10,5), (12,9,6), (12,8,7), (12,7,8),

(11,10,6), (11,9,7), (11,8,8),

(10,10,7), (10,9,8),

(9,10,8).

So he would draw a minimum of 2 greens, 4 blues and 9 yellows.