Tutor profile: Laura P.
A speech team consists of 5 students. How many groups of 3 can you make for a team photo?
This is a combination question. For permutation questions (unlike combination questions), order matters. The question is asking how many groups of three the picture could consist of (that would be a combination), NOT the number of ways the three students can be arranged (permutation). I will do this question the long way to help us understand the formulas. The combination formula is n!/r!(n-r)! n = total number of objects/people (for this question n=5) r = number of objects/people selected (for this question r=3) Imagine there are three open seats of which we need to fill from 5 people. For the first seat, there are 5 potential people who can sit down. For the second seat, there will only be four choices (because one person will already be sitting in seat one). For the third seat, there will only be three options (because two people will already be sitting in seat one and seat two). This is why we take n!/(n-r)! n! = 5*4*3*2*1 = 120 Now, because there are only 3 chairs, not 5, we only should take 5*4*3 as explained above. That is why in the formula, you divide by (n-r)! (n-r)! = (5-3)! = 2! = 2*1 n!/(n-r)! = 5*4*3*2*1/2*1 = 5*4*3 Notice how the "2*1" cancels out in the numerator and denominator. Just as stated earlier, there are only three chairs, so you should only multiple the first three numbers of n! (in this problem, that would be 5*4*3). That is why the formula works, it cancels out any parts of the numerator that surpass the number of objects/people selected (or "r") 5*4*3 = 60 Now, this 60 is the total number of possible ways we can select and order three people for a photo from a total of 5 people. Because we are just trying to figure out how many groups of three we can make (and NOT how the group is ordered), we must divide 60 by the number of ways the group of three can be ordered. This is calculated by taking r! r! = 3*2*1 = 6; so there is 6 ways we can order a group of 3 The last step is taking the total number of ways we can select AND order (60) by the number of ways we can order (6). 60/6 = 10 Our final answer is 10. The simpler way to answer this problem is simply identifying it as a combination or permutation and using the correct, memorized formula COMBINATION: n!/r!(n-r)! PERMUTATION: n!/(n-r)!
What are implicit association and implicit bias?
Implicit Association has to do with two concepts: the subconscious and memory connections in our brain. What is the first word that comes to mind when you think of TV? is it Netflix? Our brain is constantly trying to work faster. Because TV often goes with our Netflix binges, there is a strong memory association between the two. Our brain moves rapidly from TV to Netflix because these two concepts have been associated so many times previously. These connections, however, are implicit, meaning we don't always recognize we are making them. They exist in our subconscious. Many times, implicit association is a good thing, it helps our brain work faster, however, there are some connections that result in implicit bias and stereotyping. What is the first thing that comes to mind when you think of females? Is it cooking? Cleaning? Mothering? How about for men? Is it leading? working? Implicit bias occurs when we stereotype based on associations we have made due to our cultural surroundings. In the media, oftentimes the men are portrayed as working, whereas women are portrayed as staying at home. Due to this consistent stereotypical portrayal, our brain often more easily associates men with working and women with staying home. This is called implicit bias. This bias is often unconscious, meaning we don't always know it exists, nor do we recognize when our words or actions stem from such bias. Many times, we don't agree with the bias. We might think women should work, but our brain will still associate women with staying at home more quickly, due to the association that has been built through media and cultural exposure.
Compared to the mass of an object on earth, is the mass of an object on the moon the same or different?
The key part of this question is understanding the difference between weight and mass. Mass, in physics terms, identifies "how much stuff" is in an object. The amount of "stuff" does not change when you move planets, or to the moon, so the answer to the above question is "the same". Weight, however, would be different on the moon than on earth. Weight, in physics, identifies the gravitational interaction between objects with mass. Gravity on the moon is different than gravity on earth (remember the videos of Neil Armstrong bouncing as he took his first steps?) meaning the weight of an object on earth would be different than the weight of an object on the moon.
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