Permutations (2 Viewers)

[lyounamu]

All the letters of the word ENCUMBRANCE are arranged in a line. Find the total number of arrangmenets, which contain all the vowels in alphabetical order but separate at least one consonant.

Thanks in advance.

 

[dolbinau]

oh my god. Where did you get this question from?

 

[lyounamu]

oh my god. Where did you get this question from?

Amazing question isn't it? Got it from random Trial paper. I know how to do it but my method will take me roughly about 20 minutes. I want a faster method and I am sure there is.

 

[midifile]

Amazing question isn't it? Got it from random Trial paper. I know how to do it but my method will take me roughly about 20 minutes. I want a faster method and I am sure there is.

Whats the answer

 

[lyounamu]

Whats the answer

I don't know. Sorry, but my friend has it. As soon as I find out, I will post it up.

Did you get it?

 

[midifile]

I don't know. Sorry, but my friend has it. As soon as I find out, I will post it up.

Did you get it?

The only way I can think of doing it is by working out the number of arrangments where none of the vowels are next to each other, and then dividing by (4!/2!) to find the number of arrangements where they are in alphabetical order.

How many marks was it worth? It seems like way to much work for a few marks

 

[lyounamu]

The only way I can think of doing it is by working out the number of arrangments where none of the vowels are next to each other, and then dividing by (4!/2!) to find the number of arrangements where they are in alphabetical order.

How many marks was it worth? It seems like way to much work for a few marks

4 marks.

 

[lolokay]

7!/2!2! (arrange the consonanats)
8!/4!4! (arrange the vowels among them)

total = 88200

do you know if that's right?

 

[bored of sc]

total number of ways: 11!/2!2!2! = 4989600

 

[lyounamu]

total number of ways: 11!/2!2!2! = 4989600

Nah, that's not it. You have to take into account of all the things into account. That's just total number.

 

[bored of sc]

Nah, that's not it. You have to take into account of all the things into account. That's just total number.

Yeah I know. I just wanted to show how helpless I am in trying to solve it.

 

[lyounamu]

7!/2!2! (arrange the consonanats)
8!/4!4! (arrange the vowels among them)

total = 88200

do you know if that's right?

Yeah, that's right. I understand the 7!/2!2! part but I don't get 8!/4!4!.

Elaborate on this please.

 

[bored of sc]

Outstanding skills Lolokay.

 

[lyounamu]

Outstanding skills Lolokay.

This is a 4-mark question though. I don't think you can just write two lines. According to the solutions, you had to show why they are like that. There are all sorts of things that you have to account. But I think he shortened all that.

 

[lolokay]

Yeah, that's right. I understand the 7!/2!2! part but I don't get 8!/4!4!.

Elaborate on this please.

There are 8 places to put vowels. The ways of ordering the vowels equals the number of combinations of 4 from 8, as the order is given. 8C4 = 8!/4!4!

 

[lyounamu]

There are 8 places to put vowels. The ways of ordering the vowels equals the number of combinations of 4 from 8, as the order is given. 8C4 = 8!/4!4!

Yeah, I get that. Um...I really never thought of that.

 

[Michaelmoo]

Holy... What the hell is this. I hate permutations/combinations. Questions can be rather anoying as they take too long (LIKE THIS!!!) and its easy to make a silly mistake