Question

В коробке 100 жетонов, отличающихся лишь цветом: 20 красных, 20 жёлтых, 20 зелёных, 20 синих, остальные — чёрные и белые. Какое наименьшее количество же-тонов нужно взять, не глядя, из коробки, чтобы среди них обязательно оказалось не менее десяти жетонов одного цвета? А. 40. Б. 47. В. 55. Г. 61.

Answer 1

Problem Analysis

In this problem, we are given a box containing 100 tokens, which are distinguished only by their color. There are 20 red tokens, 20 yellow tokens, 20 green tokens, 20 blue tokens, and the rest are black and white tokens. We need to determine the minimum number of tokens we need to randomly pick from the box without looking, in order to guarantee that we have at least 10 tokens of the same color.

Solution

To solve this problem, we need to consider the worst-case scenario. In the worst-case scenario, we would pick all the tokens of one color first, and then start picking tokens of another color. This ensures that we have at least 10 tokens of the same color.

Let's calculate the minimum number of tokens we need to pick to guarantee that we have at least 10 tokens of the same color:

- We need to pick 10 tokens of one color. - We need to pick 9 tokens of each of the other three colors (since we have already picked 10 tokens of one color). - We need to pick 1 token of each of the remaining two colors (since we have already picked 10 tokens of one color and 9 tokens of each of the other three colors).

Therefore, the minimum number of tokens we need to pick is: 10 + 9 + 9 + 9 + 1 + 1 = 39

So, the correct answer is 39.

Answer

The minimum number of tokens we need to pick, without looking, from the box in order to guarantee that we have at least 10 tokens of the same color is 39.