A person wrote the word "SUOLAS" on a sheet of paper. How many different words can be formed by rearranging the letters of this word? How many words can be formed without the letter "S" next to each other? Answer 360
#help
vestal merlin
frosty basinBOT
regal wharf
Hey, so here do you think the arrangements would involve combinations or permutations?
vestal merlin
Hey, so here do you think the arrangements would involve combinations or permuta...
combinations
9*4!
i think this should be
regal wharf
Ie the scenario
vestal merlin
Well, it's a permutation here as order matters
yeah
regal wharf
So how many ways can 9 letters be sorted into 9 slots?
vestal merlin
So how many ways can 9 letters be sorted into 9 slots?
no you can change word order
vestal merlin
Yeah you can
so not permutation because the order is not important
regal wharf
so not permutation because the order is not important
It is permutation
Cause order matters
Let me give you an example w 3 letters
vestal merlin
why
vestal merlin
yes
vestal merlin
ok
vestal merlin
They're the same letters just different orders
9
regal wharf
The word has 6 letters.
vestal merlin
yes
regal wharf
So where's the 9 coming from
vestal merlin
but 9 ways you can change s places
regal wharf
What?
vestal merlin
and 4! other words
regal wharf
Where is the 9 comint from
vestal merlin
Where is the 9 comint from
10 ways
vestal merlin
Where are u getting the 9 and 10 from
so by changing s places
regal wharf
How does that bring in a 9 and 10 there's only 6 letters
vestal merlin
What????
SXXXXS, SXSXXX, XSXSXX, XXSXSX, XXXSXS, SXXSXX, XSXXSX, XXSXXS, SXXXSX, XSXXXS.
10 ways
regal wharf
Well instead of doing it manually let's do it mathematicall
Mathematically*
Cause manually won't work for larger numbers
vestal merlin
Cause manually won't work for larger numbers
so show me
regal wharf
Ok so
Think of this word as 6 empty slots
And you're putting 1 letter into each slot
So that's 6P1
Or 6!
But here an S is repeated, so you have to divide by 2!
That gives us the first answer
6!/2! Or 360
Now for the 2nd, we use the gap method
Since the 2 S's can't be together, let's see how many ways we can permute the leftover 4 letters into 4 slors
Which is 4!
Now with 4 of these slots , there'll be 5 gaps formed
Somethinf like
-x-x-x-x-
And now the S's can be sorted into any of these gaps without being adjacent. Ways of sorting 2 objects into 5 slots where order does matter is 5P3. Here we divide by 2! Again as the S's are repeated. Now we use fcp and multiply these 2 answrrs
So our final answer for the 2nd part should be (4!)(5!/(3!2!))
vestal merlin
And now the S's can be sorted into any of these gaps without being adjacent. Way...
so wrong answer
gritty pike
no restrictions 6!/2 permutations = 360
SS together 5! = 120
no SS together 6!/2 - 5! = 240
viscid horizon
vestal merlin
.solved