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# Arrangements Watch

1. These questions will be the death of me

1. In how many way's can the letters EIGHTEEN be arranged
2. A group of 5 first year and 3 second year students are having their picture taken standing up in a row:
i) In how many ways can they stand?
How many ways can they be arranged if:
a) all the first years stand together
b) all the first AND the second years stand together
c) None of the second years stand next to each other

Question's sound so damn easy but I really can't figure it out. :<
2. (Original post by Affection)
These questions will be the death of me

1. In how many way's can the letters EIGHTEEN be arranged
2. A group of 5 first year and 3 second year students are having their picture taken standing up in a row:
i) In how many ways can they stand?
How many ways can they be arranged if:
a) all the first years stand together
b) all the first AND the second years stand together
c) None of the second years stand next to each other

Question's sound so damn easy but I really can't figure it out. :<
do you know any formulas about permutations?
3. (Original post by TeeEm)
do you know any formulas about permutations?
Formulas? Ah, I thought you needed to work them out by using factorial notation... or am I thinking wrong?
4. (Original post by Affection)
Formulas? Ah, I thought you needed to work them out by using factorial notation... or am I thinking wrong?
well permutation formulas are factorials, so let me rephrase

if you have 8 different letters do you know how many 8 letter words, 7 letter words, 6 letter words etc can you make.

then what do you do if a letter appears twice
5. (Original post by TeeEm)
well permutation formulas are factorials, so let me rephrase

if you have 8 different letters do you know how many 8 letter words, 7 letter words, 6 letter words etc can you make.

then what do you do if a letter appears twice
If the letter appears twice... do you just ignore it? :s Since the question asked 'How many ways can the letters of EIGHTEEN be arranged', I did '6 factorial', but i'm not sure...
6. (Original post by Affection)
If the letter appears twice... do you just ignore it? :s Since the question asked 'How many ways can the letters of EIGHTEEN be arranged', I did '6 factorial', but i'm not sure...
STATISTICS

10 letters

S = triple repeat
T = triple repeat
I = double repeat

how many 10 letter words

10!/(3!3!2!)

try yours
7. (Original post by TeeEm)
STATISTICS

10 letters

S = triple repeat
T = triple repeat
I = double repeat

how many 10 letter words

10!/(3!3!2!)

try yours
8!/3! = 6720 ?
8. (Original post by Affection)
8!/3! = 6720 ?
I think so
9. (Original post by TeeEm)
I think so
Does the same apply for the other question too?
10. (Original post by Affection)
Does the same apply for the other question too?
not quite

just permutation modelling based on a handful of themes.
11. (Original post by TeeEm)
not quite

just permutation modelling based on a handful of themes.
Ah so I need to answer the second question differently from the first one? :s
12. (Original post by Affection)
Ah so I need to answer the second question differently from the first one? :s
different modelling but you can think of the students like letters
13. (Original post by TeeEm)
different modelling but you can think of the students like letters
So 5 first years and 3 seconds years would be:
8!
?
14. (Original post by Affection)
So 5 first years and 3 seconds years would be:
8!
?
treat the ones that need to be together as "one letter"
15. (Original post by TeeEm)
treat the ones that need to be together as "one letter"
Ah! So It's 2! ??
16. (Original post by Affection)
Ah! So It's 2! ??
which part of 2 are you doing?
17. (Original post by TeeEm)
which part of 2 are you doing?
I'm doing
2i) How many ways can they stand
18. (Original post by Affection)
I'm doing
2i) How many ways can they stand
sorry I missed that part

If there are no restrictions you gave the correct answer in post 13
19. (Original post by TeeEm)
sorry I missed that part

If there are no restrictions you gave the correct answer in post 13
Ah that's fine ^_^ Hmm so for part a)

a) all the first years stand together... would that be 5! ?
20. (Original post by Affection)
Ah that's fine ^_^ Hmm so for part a)

a) all the first years stand together... would that be 5! ?
firstly treat the 1st years as one lump (inseparable) and the 3 2nd years separately.

work out this perm

then how many perms can you get from the lump of 5...

etc

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