Question

Rishabh is picking out balls randomly from a box containing 60 colored balls: 15 green,12 red, 11 blue, 10 yellow, 8 black and 4 white."What is the minimum number of balls Rishabh needs to pick to ensure that he has at least 9 balls of the same color?

Answer 1

Let us take the extreme case. Suppose, you started taking out balls and all balls are of different color. 1st 6 pics will result is 6 balls of different colors.Similarly, keep picking the balls till no white ball is left(since white ball is minimum in number.)Taking the extreme case, you have picked total 6*4=24 balls in which you have 4 balls of each color.

Now, again continue the cycle, taking the worst case that each time you get a ball of different color. Do this till all black balls are over. So, now you will have 5*4=20 balls of which 4 are of same color.

Combining both the steps, now you have 4+4 = 8 balls of all colors, in 24+20=44 pickups

The next pick will give you ball of any color, which will give you 9th ball of any of the colors you have.
Hence, minimum attempt required is = 44+1 = 45 picks.