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Counting ArrangementsA password is going to be formed by rearranging (all of) the letters of the word WLLAMETTE(i) . How many total diflerent arrangements are possi...

Question

Counting ArrangementsA password is going to be formed by rearranging (all of) the letters of the word WLLAMETTE(i) . How many total diflerent arrangements are possible?How many if the two L $ must be next to each other (LL)?(iii) . How Inany if W cannot be first and E cannot be last? (So LIWMEELATT is okay; but LIWMELATTE is not.)

Counting Arrangements A password is going to be formed by rearranging (all of) the letters of the word WLLAMETTE (i) . How many total diflerent arrangements are possible? How many if the two L $ must be next to each other (LL)? (iii) . How Inany if W cannot be first and E cannot be last? (So LIWMEELATT is okay; but LIWMELATTE is not.)



Answers

How many different-appearing arrangements can be created using all the letters AAABBC?

All right. So this is where we're being us to set up a three legged password. So and but each possible cannot be repeated. So for the personal letters, 26 choices but a second letter that we cannot have the same little to force others from the five choices on 24 choices for the last one. So that's six of 1 500 for which he goes to 15,600 places.

Let's rearrange the letters in the word number and figure out how many different ways this can be done. But we have the condition where E and R must remain next to each other. They can switch orders so R E is perfectly acceptable, but they still have to be next to each other. So how many different ways can this be done? Let's consider bonding this E R together into one letter, which I'll just represent with this triangle. So that means we have essentially five letters. N u m b and triangle. So how many different ways can be ordered? These? Well, there's five different spots in our new word. And so for the first letter, there's five different possibilities than four for the next 3 to 1. And by the multiplication principle, we just have to multiply these together to figure out that there are five factorial different ways to make this new word. That is a word spelled with N. U M B and strangle. So now we just have to add in the fact that triangle can be E. R or R E. That is, there are two different options here, so we multiply our number of options. Five factorial by two different things for triangle to be. So now we have five factorial times to five. Factorial is 1 20 then multiplying by two gives us to 40. So there are 240 different ways to make this word, assuming that e and R are inseparable.

So no, from you station is involved in this particular some because you're does matter because it does matter in which Ordo no four digit would be selected. So it was very important in which harder four digit will be selected and forward or the password. So the arrangement in for the password does matter, so therefore the permutation is in one.

So no, they don't. Seven letter word. Would we have to make a password makeup password out off it from four letters which are not repeated, Are not you, Peter? So therefore there is a particular order. There's no reputation. So we will use for mutation off seven people, which will be right in seven factorial upon three factorial, which is seven, multiplied with six five, four on three factorial upon the factorial, which is close to 840 boss words can reform.


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