Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the maximum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?

Question

Mathematics

Malcolm Patterson

28 July, 07:07

Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the maximum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?

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Ernie · Answer 1

The maximum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color is:

26

Step-by-step explanation:

Since, Ben has 30 pencils in a box.

Each of the pencils is one of 5 different colors, and there are 6 pencils of each color.

This means that if he draw 24 pencils then there may be a worst case that all these pencils must be of 4 of the 5 colors and none of the pencil of the 5th color is drawn.

This means that in order to confirm that he has at least 2 pencils of each color he need to draw 2 more pencils.

This means that he need to draw: 24+2=26 pencils.