Arrangements

These questions will be the death of me :frown:

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. :<
Please help ;-; <3

Scroll to see replies

Reply 1

TeeEm

Original post by Affection

These questions will be the death of me :frown:

do you know any formulas about permutations?

Reply 2

Affection

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? :confused:

Reply 3

TeeEm

Original post by Affection

Formulas? Ah, I thought you needed to work them out by using factorial notation... or am I thinking wrong? :confused:

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

Reply 4

Affection

Original post by TeeEm

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...

Reply 5

TeeEm

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

Reply 6

Affection

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 ?

Reply 7

TeeEm

Original post by Affection

8!/3! = 6720 ?

I think so

Reply 8

Affection

Original post by TeeEm

I think so

Does the same apply for the other question too?

Reply 9

TeeEm

Original post by Affection

Does the same apply for the other question too?

not quite

just permutation modelling based on a handful of themes.

Reply 10

Affection

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

Reply 11

TeeEm

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

Reply 12

Affection

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!
?

Reply 13

TeeEm

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"

Reply 14

Affection

Original post by TeeEm

treat the ones that need to be together as "one letter"

Ah! So It's 2! ??

Reply 15

TeeEm

Original post by Affection

Ah! So It's 2! ??

which part of 2 are you doing?

Reply 16

Affection

Original post by TeeEm

which part of 2 are you doing?

I'm doing
2i) How many ways can they stand

Reply 17

TeeEm

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

Reply 18

Affection

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! ?

Reply 19

TeeEm

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 1^st years as one lump (inseparable) and the 3 2^nd years separately.

work out this perm

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

etc