<p>Hey, I took some practice sections and I had trouble with these questions:</p>
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<p>The figure above represents four offices that will be assigned randomly to four employees, one employee per office. If Karen and Tina are two of the four employees, what is the probability that each will be assigned an office indicated an X?</p>
<p>I have a feeling this would be a ratio between the number of all possibilities and combinations under the number of possible ones with the given limit. A permutation over a combination? </p>
<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?</li>
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<li><p>There are 4! = 24 ways to assign four people to the four different offices. That's the denominator. In the numerator, there are just two ways to assign Tina and Karen to the two end offices. So the probability is 1/12.</p></li>
<li><p>The worst case (most boxes selected) happens when in the first eight draws you get two of each color. The next box selected has to match one of the pairs already drawn, so 9. Right?</p></li>
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<p>If j is chosen at random from the set of {4,5,6} and k is chosen from the set of {10, 11, 12}, what is the probability that the product of j and k is divisible by 5?</p>
<p>if you choose either 4 or 6 for i and either 11 or 12 for j, the product will not be a multiple of 5. So there are 4 ways to choose a product that isn't divisible by 5. There are a total of 3*3 = 9 possibilities. 9-4=5 ways to choose a product divisible by 5. 5/9</p>
<p>There are two ways to assign karen and tina to end spaces. Either karen 1st, tina, last or other way around. There are two ways to assign the remaining two workers to the two spaces (switching hteir order). THere's 2*2=four ways in total to order the employees so karen and tina get end spaces. 24 possibilities total, so 4/24=1/6</p>
The worst case (most boxes selected) happens when in the first eight draws you get two of each color. The next box selected has to match one of the pairs already drawn, so 9. Right?
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<p>But still ... why do you have to choose 8 boxes to get two of each color? I mean, like why not 6? I didn't get the logic behind that ...</p>
<p>Another way to look at the first problem is to look at them one at a time. The chance that Tina will get a corner office is 1/2. Assuming she gets one, there are now three offices left, but only one is a corner office. So the chance of Karen getting one after Tina does is 1/3. Multiply the two numbers together to get the answer. (1/6)</p>
<p>Oh duh PoeticExplosion, that's a good way too! I never thought of that. </p>
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The worst case (most boxes selected) happens when in the first eight draws you get two of each color. The next box selected has to match one of the pairs already drawn, so 9. Right?
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But still ... why do you have to choose 8 boxes to get two of each color? I mean, like why not 6? I didn't get the logic behind that ...
<p>You're trying to find the number of boxes that will guarantee three scarves of the same color have been drawn. So you have to consider the worst case, where you have been unlucky and not got your three matches until the ninth draw.
In 1. I should have said that there are four ways that Tina and Karen can get corner offices, so the answer is 1/6.</p>