<p>Permutation has restrictions combination doesn’t.</p>
<p>Have a nice day</p>
<p>Okay cheers pckeller. Yes I know we have to multiply but I was wondering whether the nCr method worked for those really easy questions too.</p>
<p>In a sense, it does. Say there are 6 appetizers and 4 main courses. When you are doing 6 x 4, you are really doing 6C1 x 4C1. </p>
<p>If for some reason they asked: how many ways can you order 2 appetizers and 2 main courses? It would be 6C2 x 4C2 — but I beleive that exceeds SAT difficulty.</p>
<p>@pckeller</p>
<p>It is rare, but such problems do come up every now and then. I recall a problem where you need to choose 1 experienced plumber and 2 novice plumbers (or something like that).</p>
<p>The SAT does include tricky counting problems. But they are usually just twists on the counting principle. Here’s one to play with…</p>
<p>How many two-letter codes can be made using only the first 8 letters of the alphabet if letters cannot be repeated and vowels cannot follow consonants?</p>
<p>^ is it 32?</p>
<p>Btw, dr. Steve, here’s the plumber one:
CB book, 2nd edition, Test 7, pg 773, #15:
15. The Acme Plumbing Company will send a team of 3 plumbers to work on a certain job. The company has 4 experienced plumbers and 4 trainees. If a team consists of 1 experienced plumber and 2 trainees, how many different such teams are possible?</p>
<p>That question always got on my nerves… would still do it wrong again I think… (even my teacher did wrong the first time and was sure it was the cb that was mistaken… lol… i’ll never let him forget that :P) How can we know?!! So FRIGGIN" CONFUSING MAN!</p>
<p>Btw, dr. Steve, here’s the plumber one:
CB book, 2nd edition, Test 7, pg 773, #15:
15. The Acme Plumbing Company will send a team of 3 plumbers to work on a certain job. The company has 4 experienced plumbers and 4 trainees. If a team consists of 1 experienced plumber and 2 trainees, how many different such teams are possible?</p>
<p>That question always got on my nerves… would still do it wrong again I think… (even my teacher did wrong the first time and was sure it was the cb that was mistaken… lol… i’ll never let him forget that :P) How can we know?!! So FRIGGIN" CONFUSING MAN!</p>
<p>I remember the plumber question: </p>
<p>How would you use nCr or nPr in that case? </p>
<p>I see your point about the 6C1 X 4C1 </p>
<p>Also, I still don’t get what people mean when they talk about using permutations when the order is important. I dont completely understand what they mean. </p>
<p>The below is permutation question but didn’t completely understand why: </p>
<p>A security system uses a four letter password but no letter can be used more than once. How many possible passwords are there? </p>
<p>How is the above a permutation, why is it a permutation question</p>
<p>Cheers</p>
<p>Even Sal Khan did it wrong… poor dude, he sounded so sure of himself… </p>
<p><a href=“https://www.khanacademy.org/test-prep/sat-math/v/sat-prep--test-5-section-3-part-5[/url]”>https://www.khanacademy.org/test-prep/sat-math/v/sat-prep--test-5-section-3-part-5</a></p>
<p>How in the name of God, in the middle of a FOUR HOUR EXAM would someone think of doing it in any other way?! uuugh… offft :/</p>
<p>the code one is a permutation question because the order counts. as in if you have the letters: EFRT, arranging them as FERT is different than TREF… they produce different codes, so the order of them counts… </p>
<p>but the nb of ways to choose 2 hats from Red, green, and blue hats for example is a combination simply because choosing a red then green hat is the same as choosing a green then red hat…</p>
<p>this is what we mean when we say “order counts” </p>
<p>get it?</p>
<p>If you do know nCr…</p>
<p>It’s 4C1 x 4C2</p>
<p>But you could also call the plumbers A, B, C, D and the trainees p, q, r, s…</p>
<p>When you do problems by listing, be organized and you will save time. </p>
<p>For example, after listing Apq, Apr, Aps, Aqr, Aqs and Ars, you can just take those 6 and multiply by 4.</p>
<p>As for the other one I gave you about the two letter codes, I got more than 32…but maybe I did it wrong :)</p>
<p>For the plumbing problem, there are 4C1 ways to choose 1 experienced plumber from 4, and 4C2 ways to choose 2 trainees from 4. By the counting principle, the answer is (4C1)(4C2) = (4)(6)=24.</p>
<p>Khan’s mistake in the video is that he is using permutations instead of combinations. Selecting trainee E followed by trainee F is the same as selecting trainee F followed by trainee E. His math doesn’t account for this which is why his answer came out to double the correct answer.</p>
<p>Okay so here are my answers to your questions :)</p>
<p>Combo: 10 </p>
<p>Perm: 1/34650 (I got 1/ 39,916,800 first time round)</p>
<p>Working for perm </p>
<p>total combinations 11P11 with any arrangement </p>
<p>For just Mississippi: </p>
<pre><code> ---------- (I hope that’s 11 spaces)
</code></pre>
<p>1 for first box
4 for second (4 possible I’s)
4 for third (4 possible S’s)
3 for fourth (3 possible S’s)
3 for fifth (3 possible I’s)
2 for 6th box (2 S’s remaining)
1 for 7th box (1 s remains)
2 for 8th box
2 for 9th (2 P’s)
1 for 10th
1 for 11th </p>
<p>Let me know if this was the right working </p>
<p>Cheers</p>
<p>Thanks Dr Steve for the lucid explanation. I will add it to my combination and permutation notes. I think I have the hang of it now though! The notion of ordering is still a little fuzzy though :)</p>
<p>and my calculation was: </p>
<p>1 X 4 X 4 X 3 X 3 X 2 X 1 X 2 X 2 X 1 X 1 / total</p>
<p>^coolio! they are both correct…
well then, there ya go… u’re getting the hang of it 
of course, these will prob never show on SAT 1… especially Mississippi… lol… (now the English teachers should really give us a break… if they just knew probability :/… hahahaha) </p>
<p>Now you just have to practice some more… there are a ton online, khan academy i guess…
would u like me to give u some?</p>
<p>and don’t worry… it’s just lately that they became less fuzzy to me too… I hope i don’t get one in the SAT, screw it up, and come here crying :@ </p>
<p>Btw, do u know any of those tough SAT probs? like the toughest u faced? i’d like to know what i may be up to and not get the shock like in Nov 2012… that was a shocker, man… can’t get over it -_-’’</p>
<p>2200andbeyond, thanks for the offer (the examples) but no thanks. I think I have done enough for today! If I do feel I need more practice though, I will check online and check the Khan academy. </p>
<p>I think you should be fine for the Jan SAT; you have obviously practiced a lot and so now just play the waiting game. Relax take and take it easy. I’m sure the November 2012 was just a one off thing. Just get psyched and try to go in the exam with an open mind. I know I am </p>
<p>As for hard problems, from what I can remember all the hard questions are pretty much the same and there hasn’t been one that I have faced and been completely shocked. If you have practiced, level 5 problems should be okay. If you get stuck on it in the exam, just skip- that’s what i’ll do! </p>
<p>Take it easy mate</p>
<p>Here’s a challenging counting problem if you’d really like to sharpen your permutation/combination skills. Note that this is much harder than any problem that will ever appear on an SAT:</p>
<p>Let j and k be positive integers with j≤k. In how many ways can k be written as a sum of j positive integers?</p>
<p>Hint: The answer can be written as either aPb or aCb for some a and b.</p>
<p>^ doesn’t it depend on the value of the variables?
u sure that’s it?</p>