grace has 16 in her pocket. she has 8 red ibesm 4 green ones, and 4 blue ones. what is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
The worst case is that she draws:
8 reds, followed by
4 greens (still no blue yet).
Can you take it from here?
is the answer 12?
With 12, and in the worst case, you only have two colours. So how many do you need to get the third colour?
To find the minimum number of jellybeans Grace must take out of her pocket to ensure that she has one of each color, we can follow these steps:
1. Determine the maximum number of jellybeans of each color that Grace can pick without having one of each color. In this case, the maximum is 8 (red), 4 (green), and 4 (blue), as she has 8 red jellybeans, 4 green jellybeans, and 4 blue jellybeans.
2. Calculate the total number of jellybeans she can take without having one of each color. This can be done by adding the maximum number of each color: 8 + 4 + 4 = 16.
3. Since Grace has 16 jellybeans in her pocket, if she takes out all the jellybeans without getting one of each color, she would have picked out all the jellybeans without success.
Therefore, the minimum number of jellybeans Grace must take out of her pocket to ensure that she has one of each color is 17 (16 jellybeans without having one of each color + 1 additional jellybean to guarantee that she has one of each color).