<p>A teacher is to be assigned to teach 5 different courses in 5 different class periods on Mondays. If exactly one course meets each period, how many different assignments of courses to these class periods are possible for Mondays?
Answer: 5<em>4</em>3<em>2</em>1
I didn't know the answer at first, I stupidly added 5+4+3+2+1. </p>
<p>I made this similar question to see if it's same way the first one is solved.</p>
<p>If I have 4 PCs and each PC goes with a keyboard, which I also have 4 of. How many ways can I arrange a PC and a keyboard?
So, I think this is how you do it: 4<em>3</em>2*1 ?
Am I right? I suck at combination/probability/permutation questions, and so I wanted to know how you solve these types of questions.</p>
<p>No, the first is right because you can essentially make a table. One row x 5 columns (one for each class period). Now, you have 5 choices for the first period. Then you only have 4 choices left for the second period (no two courses are the same, we are assuming), and so on. So, 5x4x3x2x1. You never add for these type of questions; always multiply. </p>
<p>Your second one is more complex. If you have four different PCs and four different keyboards, then there are 16 different combinations. But if you’re selecting one after another, it is slightly more difficult and I don’t remember how to solve it.</p>
<p>I think ccuser had it right. If the question was “how many pc-keyboard pairings are possible?” the answer would be 16: you would choose from 4 pcs and then choose from 4 kbs. </p>
<p>But if the question is: “4 pcs must each be matched with 4 kbs. In how many ways can this be done?”, then the answer is 4x3x2x1. Here’s why:</p>
<p>Pick a computer. You have 4 choices of kb. Now pick the next computer. You now have only 3 choices of kb…and so on.</p>
<p>Both versions are SAT-like and both can be solved just using this counting principle.</p>
<p>A restaurant serves 5 types of burgers, 4 types of fries, 4 types of salads, and 3 kinds of drinks. How many different meals can you order consisting of a burger, fries, salad and a drink?</p>
<p>How many different orders are possible if you can order no more than one of anything (but don’t have to order one of each)? </p>
<p>I think that second one has a twist that makes it un-SAT-like, but I won’t say anything just yet…</p>
<p>There is a reason fast food restaurants’ workers are clamoring for a 15 dollars minimum hourly wage. Soon you will need a PhD in Math from MIT to serve a meal. Actually, more than a few already have similar degrees. :)</p>
<p>I have not seen anything like your second questions on an SAT, but I’m not 100% sure that it would never show up. I think it would need to be worded more carefully.</p>
<p>One thing might not be completely clear - does something have to be ordered? The English definition of “order” would seem to indicate yes, but the mathematical definition of an “order” perhaps contains the empty order?</p>
<p>As always, Dr Steve is on the money – that is exactly the issue that in my mind disqualifies this as an SAT question, or at least requires a clear statement in the posing of the question. Is an order of nothing an order? It’s a Zen thing…</p>
<p>Still, to keep the question viable, I’ll stipulate: a diner orders SOMETHING. </p>
<p>In any case, I do like the question. Without giving it away, I’ll say that I can think of a verrrrry ugly, deal-with-separate-cases approach or a nice, clean one-swoop method.</p>
<p>A restaurant serves 6 types of burgers, 5 types of fries, 5 types of salads, and 4 kinds of drinks. How many different meals can you order consisting of a burger, fries, salad and a drink? How many different orders are possible if you can order no more than one of anything (but don’t have to order one of each)? </p>
<p>All the additional choices represent a NULL choice. So you have 5 burger and a NO burger as option for a total of 6. And the same for the other choices.</p>
<p>Question is what happens to a … complete null order?</p>
<p>Oops - I think that my question ruined your presentation of the problem. Sorry about that. </p>
<p>It’s a nice problem that shows that a statement can be different in the English language than it is in standard mathematical language.</p>
<p>An even simpler example is the word “or.” In mathematics “or” usually means “inclusive or” (“xor” is reserved for “exclusive or”), but in English the word “or” may be inclusive or exclusive depending on the rest of the sentence. </p>
<p>I think I might be rambling - I’m not even sure why I started talking about this. :)</p>
<p>DrSteve - Not at all. It was all right on target. And I think the wordiness it takes to pose the question properly is what would disqualify it. Real SAT questions have a crisp economy to their presentation. That’s what threw me on another thread. An sat2 question had a weird redundancy. But it was in fact college board.</p>
<p>I believe the other thread you’re talking about involved a logic question? I think the situation is different there, and I sort of understand why the College Board made the question that way.</p>
<p>I only skimmed the thread, but I think your issue was something like “why is the college board making a big deal about whether one statement follows from the other if the invalid statement also happens to be the only false one?”</p>
<p>I can kind of see your point, but in my mind since validity has little to do with truth, I don’t see why it matters that “false” and “invalid” happen to line up nicely. I guess it just makes the question easier because students who “fall into the trap” of picking the false one will actually get the question right.</p>
<p>But in any case, that question doesn’t particularly bother me (as long as I read it correctly), whereas this one would if I saw it on an SAT (unless it was worded very carefully).</p>
<p>I hope I know what I’m talking about here since I’m making comments about a thread I didn’t read very carefully. I probably should have looked up that thread before talking about it, but I’ve had a very busy day, it’s late, I have a headache, and mostly I just didn’t feel like looking for it.</p>
<p>SATQuantum is correct, but I just want to rephrase it another way (his way is also fine if you understand it):</p>
<p>By observation, a horizontal line seems to be a good fit for the data. A horizontal line has equation y=constant. In this case the constant is 44. So y=44 best fits the data. Here t(p) is being used in place of y, so the answer is t(p)=44.</p>
<p>@xiggi
For the question:
A restaurant serves 5 types of burgers, 4 types of fries, 4 types of salads, and 3 kinds of drinks. How many different meals can you order consisting of a burger, fries, salad and a drink?
How many different orders are possible if you can order no more than one of anything (but don’t have to order one of each)? </p>
<p>Do you mean the answer would be: 6<em>5</em>5*4 ?</p>
<p>In the xy plane, equation of line l is y=3x-1. If line m is the reflection of line l in the y axis, what is the equation of m?
A) -3x-1
B)-(x/3)-1
I eliminated the other choices by guessing that the slope of m is negative and y intercept is -1. But how do I find the correct equation between these two?</p>
<p>One simple way is to just pick 2 points on the original line, say (0,-1) and (1,2), and then reflect these points in the y-axis. You get the points (0,-1) and (-1,2).</p>
<p>Now compute the slope of the line passing through these 2 points. You can do this visually (to get from (-1,2) to (0,-1) you move down 3, right 1) or by using the formula m = (2-(-1))/(-1-0) = 3/(-1) = -3. So the answer is (A).</p>
<p>Note that choice (B) is the “trap” answer. Many students think that when you reflect a line in the x- or y-axis you get a line perpendicular to the original. This is almost always false. The angle formed from these 2 intersecting lines is almost never 90 degrees.</p>