Permutations with Identical Items help

jijie14

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How many different ways to arrange the word STATISTICAL if
a) the S's are together

for this one, i didnt know if I should just multiply the rest by 1 since the S's are the same or do 2x1 .
the rest is just the S's x 10 x 9!/3!2!2!

b) the S's not together

when i get my answer from part a , i'm gonna find the total possibilities of arrange the word which is 11!/3!2!2!2! = 831600 then subtract that with answer part a which i hope will give me the S's not together

c) the two S's together and two 1's together

for this one, i was thinking of doing two cases; 1 for just the two s's then the other for two i's together then just add those two, but then now it doesnt make sense to me :S
 
How many different ways to arrange the word STATISTICAL if
a) the S's are together

for this one, i didnt know if I should just multiply the rest by 1 since the S's are the same or do 2x1 .
the rest is just the S's x 10 x 9!/3!2!2!

b) the S's not together

when i get my answer from part a , i'm gonna find the total possibilities of arrange the word which is 11!/3!2!2!2! = 831600 then subtract that with answer part a which i hope will give me the S's not together

c) the two S's together and two 1's together

for this one, i was thinking of doing two cases; 1 for just the two s's then the other for two i's together then just add those two, but then now it doesnt make sense to me :S
I am assuming that you must use all the letters.

Always a good idea to start with a simple example.

GAGA versus GONE

In "gone" I get 4 * 3 * 2 * 1 = 24.

In "gaga" I get ggaa, gaga, gaag, agga, agag, aagg, or 6. What explains the difference? Think for a moment if one of the g's was red and one blue and one of the a's was red and one blue.

Then I would get ggaa, ggaa, ggaa, ggaa, etc = 24. 6 = 4! / (2! * 2!). The permutations of the same letter in the same spots but with different colors become invisible when they are the same color.

How many distinct 11-letter strings can you make by using all 11 letters in the word STATISTICAL?

How many distinct 9-letter strings can you make using all 9 letters in that word except S?

How many places can you modify each 9-letter string by adding or inserting SS?

Do you now have enough information to answer your two questions?

If so, what are the answers?
 
How many different ways to arrange the word STATISTICAL if
a) the S's are together
Treat the "SS" as a single letter. "(SS)TATITICAL" has 10 "letters" but three of them are indistinguishable "T"s, 2 are indistinguishable "A"s and 2 are indistinguishable "I"s. Imagine "labeling" those letters so they were "T1", "T2", and "T3", "A1" and "A2", and "I1" and "I2". Then there would be 10 distinct "letters" and so 10! permutations. But there are 3!= 6 ways to interchange just the "T"s, 2!= 2 ways to interchange just the "A"s and 2!= 2 ways to interchange just the "I"s. Since you don't want to count those as different permutations, you want to divide by those numbers.

for this one, i didnt know if I should just multiply the rest by 1 since the S's are the same or do 2x1 .
the rest is just the S's x 10 x 9!/3!2!2!

b) the S's not together

when i get my answer from part a , i'm gonna find the total possibilities of arrange the word which is 11!/3!2!2!2! = 831600 then subtract that with answer part a which i hope will give me the S's not together
Yes, that sounds like a good plan.

c) the two S's together and two 1's together
There are no "1's". Did you mean "I"s? If so treat the two S's and the two I's as a single letter. You have 9 "letters" in which there are 3 "T"s and 2 "T"s.
 
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