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An alphabet is a standard set of letters that represent the phonemes (basic significant sounds) The Greek word was made from the first two letters, alpha(α) and beta(β). The names for the Even after the fall of the Roman state, the alphabet survived in intellectual and religious works. .. A to Z (PDF). Broadway Books.
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What we are really doing is just rearranging the elements of the codomain, so we are creating a permutation of 8 elements. There are 8 choices for where to send 1, then 7 choices for where to send 2, and so on. We multiply using the multiplicative principle. This is just like the problem of permuting 4 letters, only now we have more choices for each letter. For the first letter, there are 6 choices. For each of those, there are 5 choices for the second letter.

Then there are 4 choices for the third letter, and 3 choices for the last letter. For example.

Two-Letter Words

Note that it doesn't make sense to ask for the number of bijections here, as there are none because the codomain is larger than the domain, there are no surjections. But for a function to be injective, we just can't use an element of the codomain more than once. We need to pick an element from the codomain to be the image of 1. There are 8 choices. Then we need to pick one of the remaining 7 elements to be the image of 2. Finally, one of the remaining 6 elements must be the image of 3.

We don't mean it like a combination lock where the order would definitely matter. Perhaps a better metaphor is a combination of flavors — you just need to decide which flavors to combine, not the order in which to combine them. To further illustrate the connection between combinations and permutations, we close with an example.

You decide to have a dinner party. Even though you are incredibly popular and have 14 different friends, you only have enough chairs to invite 6 of them. What if you need to decide not only which friends to invite but also where to seat them along your long table? How many choices do you have then? You must simply choose 6 friends from a group of Here you must count all the ways you can permute 6 friends chosen from a group of Notice that we can think of this counting problem as a question about counting functions: how many injective functions are there from your set of 6 chairs to your set of 14 friends the functions are injective because you can't have a single chair go to two of your friends.

How are these numbers related? In both counting problems we choose 6 out of 14 friends. For the first one, we stop there, at ways. Alternatively, look at the first problem another way. We want to select 6 out of 14 friends, but we do not care about the order they are selected in. To select 6 out of 14 friends, we might try this:. This is a reasonable guess, since we have 14 choices for the first guest, then 13 for the second, and so on. It distinguishes between the different orders in which we could invite the guests.

To correct for this, we could divide by the number of different arrangements of the 6 guests so that all of these would count as just one outcome. How many 3-topping pizzas could they put on their menu? Assume double toppings are not allowed. How many total pizzas are possible, with between zero and ten toppings but not double toppings allowed? The pizza parlor will list the 10 toppings in two equal-sized columns on their menu.

How many ways can they arrange the toppings in the left column? A combination lock consists of a dial with 40 numbers on it. To open the lock, you turn the dial to the right until you reach a first number, then to the left until you get to second number, then to the right again to the third number. The numbers must be distinct. How many different combinations are possible?

Despite its name, we are not looking for a combination here.

From A to Z: a tour of the alphabet

The order in which the three numbers appears matters. Which of the above counting questions is a combination and which is a permutation? Explain why this makes sense. How many triangles are there with vertices from the points shown below? Note, we are not allowing degenerate triangles - ones with all three vertices on the same line, but we do allow non-right triangles. Explain why your answer is correct. We must pick two of the seven dots from the top row and two of the seven dots on the bottom row. However, it does not make a difference which of the two on each row we pick first because once these four dots are selected, there is exactly one quadrilateral that they determine.

In particular, parallelograms are trapezoids. You need to skip exactly one dot on the top and on the bottom to make the side lengths equal. IMHO, the value of word scrambles and word find puzzles as homework is suspect. They may help with spelling, I suppose, and definitions in some formats, but appear to have little to offer in terms of helping students better understand and apply concepts. So, if using your resource helps students complete "busy work" assignments more efficiently, hurrah for time management!

Lesson Plans for ESL Kids Teachers

It's been shared with others who "get stuck". My daughter calls it my word cheater, I call it assistance when necessary!

Very easy to understand the results and we love it! Thanks so much!

English Alphabet

I seem like a pro playing scrabble online. This site is my little secret weapon. Helped me get extra credit in school with brainteasers! Bookmarked, shared and enjoyed! Thanks for letting us smile and conquer a difficult homework. Googled "word finder" and came here because of description, "find words for poetry. Wonderful site!!! I've bookmarked it and will come back when I need words while writing poetry.

Thank you!

I always wanted an Atari Transputer. Had the ST line and loved it for it's day. You've shared your talent and have helped a lot of people. Blessings to you. Thank you. Great site - crypto doer paradise ". Because of the way I wrote the code, it may not list every combination of the same two words it finds. Sorry about that.

Practical tips for teaching the alphabet and answers to common questions - Gift of Curiosity

I'm always trying to come up with ways to improve the code so I'll give that some thought. Brain freeze, helps to thaw it. It wasn't shown in results I just tried it and it works. Otherwise, it tries to unscramble it as a single word. It also unscrambles as "coed caretaking" and "certain dockage". My computer beat your computer.

I will use the site in the future when I am up against it!! The first word list contains all of the officially allowable Scrabble words. The second word list is for spell checking documents. There are many obscure words that are not in either list. I am working on additional word lists. If you entered a valid email, I'll let you know when it works. Otherwise, it tries to find those three letters next to each other.

Didn't you have the "any order" box checked to find "Octahedral"? Its Freakonomics. That explains why it wouldn't be in either word list.