Question

A bag contains 8 red balls, 10 blue balls, 17 green balls. what is the minimum number of balls that needs to be taken out from the bag to ensure getting at least one ball of each colour

a) 19 b) 18 c) 28 d) 27​

Answer 1

Answer:

19 balls.

Step-by-step explanation:

Step : 1 When we combine 8 red balls with 10 blue balls, we get 18 balls of two colours. However, we still need one more colour, so we take a different colour ball, making the final result 19.

Step : 2 Eight red balls, ten blue balls, and seventeen green balls are in a bag. How many balls must be removed from the bag at a minimum to ensure that each colour is represented by at least one ball? When we combine 8 red balls with 10 blue balls, we get 18 balls of two colours. However, we still need one more colour, so we take a different colour ball, making the final result 19.

Step : 3  A bag contains eight red balls, ten blue balls, and seventeen green balls. If each colour is represented by at least one ball, how many balls must be taken out of the bag at the very least? We obtain 18 balls of two colours when we mix 8 red balls and 10 blue balls. The ultimate number is 19, but we still need one more colour, so we grab a different colour ball.

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Answer 2

Choice (d) is the right response.

We must take into account the worst-case scenario, in which we select all the balls of one or two colours before receiving a ball of the third colour, in order to guarantee that at least one ball of each colour is chosen. In order to guarantee that we get a ball of each colour, we must determine the minimum number of balls to remove.

The worst case is to choose every blue and green ball before choosing a red ball because red balls are the rarest. Therefore, we must choose all 27 balls, or all 10 blue balls and all 17 green balls. Then we can be sure that we've chosen at least one ball from each colour.

In order to guarantee to get at least one ball of each colour, the minimum number of balls that must be removed from the bag is 27.

Keep in mind that we need to eliminate fewer balls if the red ball appears earlier in the process. If we choose a red ball first, for instance, we only need to choose 16 more balls to guarantee that we get one of each colour.

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