<p>I seem to always get these permutation questions wrong. I keep using the same approach- sometimes it works sometimes it doesn't. I got the easy question below wrong. I will outline my approach and would like feedback on what approach I should be using. In the Gruber's math workbook they say to use factorial method 4C3 = 4!... I don't know this method but If someone could help me on how best to improve. </p>
<p>Q. A bakery sells 4 different types of bread. How many combinations of 3 different types of bread can a customer buy from this bakery? </p>
<p>Labelled the 4 different breads A,B,C,D </p>
<p>put 3 boxes like: _ _ _ </p>
<p>In the first box we can have 4 combinations i.e. A,B,C or D
In the second box we can have 3 because have to be different
In the third box we can have 2 because 2 letters are left </p>
<p>So: I did 4 X 3 X 2 = 24 combinations. PS I know this answer is wrong the answer is 4 and I do not want a solution to the problem but an approach that works generally universally.</p>
<p>Does anyone know a method e.g. the permutation/factorial method that has worked for them all the time. </p>
<p>Ohh well, let me tell you that permutations and combinations can sometimes be a pain in the butt. Lets see, here he asked you for a combination as in you’re making a subset out of the bigger set
what you did was not wrong at all but there’s one more step, when you’re making a combination you have to divide by the number of places factorial because you don’t want repetition … example : If we have 4 places you have to divide by 4 x 3 x 2 x 1 . In our case we have three places so you’ll divide by 3 x 2 x 1
So that’s 4 x 3 x 2 / 3 x 2 x1
I hope you understand im not a native English speaker so it’s kinda hard for me to communicate</p>
<p>If you want a more lazy/test day rush method :
On your calculator there is a button called nCr just type 4 shift nCr 3 you’ll get the right answer </p>
<p>There is also an nPr but this one is for permutations not combinations</p>
<p>Yes indeed it will always work but i prefer that you understand and master the other method too.
Did you even find the nCr button on your calc ?</p>
<p>Yea no worries I have taken statistics in year 12 so yes I have dealt with permutations before and so know the nCr button. </p>
<p>Also, I looked up online and this site mentioned that there is a difference between a permutation and a combination. For combinations you must use: </p>
<p>n!/r!(n-r)!</p>
<p>For permutations you must use: </p>
<p>n!/ (n-r)! </p>
<p>Which is of the above refers to the nCr method. </p>
<p>Why do we is a permutation different from a combination; I thought they were the same but apparently they are not. </p>
<p>^U took statistics?
I get u, man… they used to always confuse me too (still a lil)</p>
<p>here u go:
Permutation: order counts, as in the order is need… like for example the number of arrangements of a letters REDF for example…
REFD is not like EFDR… so the order is important</p>
<p>Formula: n!/ (n-r)!
On calculator: nPr</p>
<p>Combination: the order is not important… as in the arrangements of the choices is not important. Example: the nb of ways u can choose 6 hats… choosing a red then black hat is not different than choosing a black then red hat… </p>
<p>Example for Combination:
You want to buy 3 hats from a selection of 5. How many possible choices do you have?</p>
<p>Example for permutation:
A word consists of 1 M, 4 I’s, 4 S’s, and 2 P’s. If the letters are randomly arranged in order, what is the probability that the arrangement spells out Mississippi?</p>
<p>These are examples, solve them, and tell me to give u the answers
Then amma give ya some mixed ones if u’d like… that way helped me a lot… step by step :)</p>
<p>Yea, in fact, I have taken statistics at university, so I don’t remember or dont know the fundamentals lol </p>
<p>Cheers 220andbeyond- the above explanations really help. A combination question was the reason why I couldn’t get 760 on the latest test I took lol. </p>
<p>Yea, if you you could put some examples up that would be great. Unfortunately I haven’t compiled a list of all the combination and permutation questions! Thanks a lot</p>
<p>do u have any advice for math for me too?! i always make those stupid mistakes… in prc tests, am getting 2-4 mistakes! any suggestions (other than concentrate… lol )</p>
<p>I’ll do the problems soon and let you know.
Well, I read the question out loud (like whispering sort of) and underline and read every sentence. I also find showing all my working and doodling on the space below has helped me cut out the stupid errors. If you are leaving lots of blank space for lots of questions then you need to show more working; it is as simple as that</p>
<p>If you know about nCr and nPr that’s great – combinatorics is an especially fascinating branch of mathematics. But you do NOT need that on the SAT. You do need the counting principle. But any SAT problem that seems to require advanced combinatorics can also be done some easier way. Listing and counting is often the quickest but thinking and playing also helps.</p>
<p>For example, let’s look at the problem that started this thread:</p>
<p>Q. A bakery sells 4 different types of bread. How many combinations of 3 different types of bread can a customer buy from this bakery? </p>
<p>Labelled the 4 different breads A,B,C,D </p>
<p>Now stop and think: choosing 3 types of bread to buy is the same thing as choosing ONE type NOT to buy. And how many ways are there to do that? 4. All done.</p>
<p>Now, you could come up with example problems where there was no “quick” way, where advanced methods were required – but they would not be SAT questions!</p>
<p>nice way, stratigicfiasco… I ended up doing the same thing… they tell u to use shortcuts on SAT; I do that… But i also write everything (almost at least) down… makes me make a lot fewer mistakes… altho i still do get 2-4 wrong now… and Jan is in days… I am DYING for an 800 man…
So anyway… without writing stuff down, i wudn’t have come this far to start with so… keep it up! :D</p>
<p>Thanks pckeller for your points. My only concern about what you stated above is that I often find that listing all the possibilities is tedious and time consuming for me. This is one of the only questions that wasn’t so cumbersome to do. </p>
<p>I look over the above comments in more detail soon</p>
<p>I recommend that as you practice counting problems you try each one in up to 3 ways:</p>
<p>(1) By listing: this way is the most time consuming, but as you practice you will get quicker at it. Also, by practicing writing lists you will practice seeing patterns and you will learn how to list in such a way that you don’t accidentally miss anything or list anything twice. Finally, by practicing listing, you will find the quicker methods below start to make more sense. There have been a few Level 5 problems on past SATs where listing is really the best way to go.</p>
<p>(2) By using the counting principle: This is a quick efficient way to solve lots of counting problems</p>
<p>(3) If applicable, by using the nPr of nCr button in your calculator.</p>
<p>what about this basic question how would you use the ncr method here</p>
<p>On a restaurant menu there are there are appetizers and 4 main courses. how many different dinners can be ordered if each dinner consists of one appetizer and one main course? </p>
<p>This is as straight-forward an example of a counting principle problem as you will ever see. It is not an nCr question.</p>
<p>You have a certain number of choices for one thing and then a certain number of choices for another thing, completely independent of the first thing. Just multiply…</p>
</p>
