Perms and combs question (1 Viewer)

[carrotsss]

b) Find the number of ways in which the letters of the word TRIANGLE can be arranged in a
line...
i) so that all the vowels are next to each other?

My working:
6 (assuming vowels are in a group of 3, this group can be in 5 places along the 8 letter row) * 3! (order of vowels within that group of 3) * 5! (order of consonants within remaining spots) = 4320

However the correct answer was:
2! × 3! × 5! = 1440

Where did I go wrong? Q is from 2020 Caringbah prelim

 

[jimmysmith560]

There is a chance that your answer is actually correct and that the paper's answer is not (perhaps someone more knowledgeable than me could confirm this). Here, I refer to working from different sources. Here is the first example:



The second example is as follows:

The number of letters in given word is 8, here 1 each are T’s, R’s, I’s, A’s, N’s, L’s, G’s & E’s. Using permutation, we have the number of words in which vowels occurs together:



I hope this helps!

 

[carrotsss]

There is a chance that your answer is actually correct and that the paper's answer is not (perhaps someone more knowledgeable than me could confirm this). Here, I refer to working from different sources. Here is the first example:

View attachment 36231

The second example is as follows:

The number of letters in given word is 8, here 1 each are T’s, R’s, I’s, A’s, N’s, L’s, G’s & E’s. Using permutation, we have the number of words in which vowels occurs together:



I hope this helps!

Thanks! Yeah I’m really not sure, usually I can easily figure out where I went wrong with these questions but this one really threw me…

 

[Life'sHard]

I remember Caringbah had some sus solutions when I was revising (or maybe a different school lol) by the looks of it it should just be 6! * 3! so your answer would be correct.

 

[fx82au]

im legit doing this exact question rn, and i thought i was going crazy. thankyou mr carrotsss