There are 30 pieces of 4 different colours but same size balls in a bag.
Asmo is asked to take out balls from the bag with closed eyes. To guarantee
the balls taken are not less than 5 same colour balls, at least how many balls should be taken out from the bag?
Suppose 4 of each color were drawn. That makes 16 balls.
The 17th ball would have to be the 5th of one of the colors.
To guarantee that Asmo takes out at least 5 balls of the same color, we need to find the worst-case scenario where Asmo selects the minimum number of balls of a single color each time.
Since there are 4 different colors, we want to make sure that Asmo picks 5 balls of one color before selecting any other colors.
Therefore, the minimum number of balls Asmo needs to take out is calculated by multiplying the number of colors (4) by the minimum number of balls needed for each color (5), which equals:
4 colors x 5 balls = 20 balls.
So, at least 20 balls should be taken out from the bag to guarantee that Asmo selects at least 5 balls of the same color.
To find out the minimum number of balls that need to be taken out to guarantee getting at least 5 balls of the same color, let's analyze the worst-case scenario.
Assume that in the worst-case scenario, Asmo picks balls in such a way that he gets the maximum variety of colors. In other words, Asmo wants to create a situation where he picks the balls of all four colors as many times as possible before reaching 5 balls of the same color.
In this scenario, Asmo can pick at most 4 balls of each color before reaching the minimum guaranteed threshold of 5 balls of the same color. So, the maximum number of balls he can pick without reaching 5 balls of the same color is:
4 color options * 4 balls of each color = 16 balls
Therefore, Asmo can pick up to 16 balls without getting 5 balls of the same color. However, to guarantee collecting at least 5 balls of the same color, he needs to pick the number of balls that exceeds this number, which is:
16 balls + 1 extra ball = 17 balls
So, to guarantee picking at least 5 balls of the same color, Asmo needs to take out a minimum of 17 balls from the bag with closed eyes.