<p>Hello all, this type of problem which I think is probability is a type I run into a lot and can't seem to get during my practices. It usually involves a set of different possibilities and 'what is the least number that must be taken out' to gain a desired number of a set.
Can someone please explain to me what this type of problem is and how to solve it. The problems I'm talking about are like the ones below.</p>
<hr>
<ol>
<li>There are 6 red, 6 brown, 6 yellow, and 6 gray scarves
packaged in 24 identical, unmarked boxes, 1 scarf per
box. What is the least number of boxes that must be
selected in order to be sure that among the boxes
selected 3 or more contain scarves of the same color?
(A) 3
(B) 6
(C) 7
(D) 8
(E) 9</li>
</ol>
<p>The problem basically says, how many scarves must we pick to have a 100% chance of there being 3 or more of the same color. All we have to do to disprove an answer choice is give a scenario in which there are 2 or less of the same color, based on the number of scarves we’re choosing.</p>
<p>3 scarves
We could have 1 red, 1 brown, 1 yellow scarf so A is wrong</p>
<p>6 scarves
We could have 2 red, 2 brown, 1 yellow, 1 gray so B is wrong</p>
<p>7 scarves
We could have 2 red, 2 brown, 2 yellow, 1 gray so C is wrong</p>
<p>8 scarves
We could have 2 red, 2 brown, 2 yellow, 2 gray so D is wrong</p>
<p>E is left as the correct answer. Even if we tried to minimize the number of repeating colors, at best we’d have 3 of the same color and 2 each of the rest (3+2+2+2 =9).</p>
<p>Answer is 9.</p>
<p>Assuming you have the worst luck, you pick one of every color…(Let R = red, B = Brown etc)</p>
<p>1st round: RBYG (4 boxes, 1 of each color)
2nd round: RBYG (4 boxes, 2 of each color now)</p>
<p>Now on the 9th pick, it doesn’t matter which box you choose as you’ll have 3 of any color.</p>
<p>So 9.</p>
<p>i was wrong there are 4 kind of scarves woops</p>