Question: please provide explanations for each below 1. [10 Points] We have a box of red, green, blue, yellow, and brown pencils, with 10 pencils of

please provide explanations for each below

1. [10 Points] We have a box of red, green, blue, yellow, and brown pencils, with 10 pencils of each color. (a) In the dark, how many pencils must we take out of the box to guarantee that we have at least 9 red, or 7 green, or 5 blue, or 3 yellow, or 1 brown? (b) How many pencils must we take to guarantee at least 7 green or 5 blue? (c) How many pencils must we take to guarantee 9 red? (d) How many pencils must we take to guarantee that we have two different colors? (e) How many pencils must we take to guarantee at least 1 of each color

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