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Permutations question HELP!!!!

Hi
I'm really stuck on this questions on permutations. I can't remember the beginning of the question but all the different parts are related to finding arrangements of letters using the word STATISTICS.
a) how many ways can the letters in the word STATISTICS be arranged
b) how many ways are there of arranging the letters so all the S's are next to each other
c) what is the probability of all S's being next to each other
d) in how many ways are there of arranging the letters so all the vowels are next to each other
e) what is the probability of the word ending in T
f) Find the probability that the first three letters spell CAT.

if there is anyone that can help me i would really appreciate it. :smile::smile:
Reply 1
Avatar for TeeEm
TeeEm
19
Original post by Saliha I
Hi
I'm really stuck on this questions on permutations. I can't remember the beginning of the question but all the different parts are related to finding arrangements of letters using the word STATISTICS.
a) how many ways can the letters in the word STATISTICS be arranged
b) how many ways are there of arranging the letters so all the S's are next to each other
c) what is the probability of all S's being next to each other
d) in how many ways are there of arranging the letters so all the vowels are next to each other
e) what is the probability of the word ending in T
f) Find the probability that the first three letters spell CAT.

if there is anyone that can help me i would really appreciate it. :smile::smile:


do you mean you cannot do any of this !!??
Original post by Saliha I
Hi
I'm really stuck on this questions on permutations. I can't remember the beginning of the question but all the different parts are related to finding arrangements of letters using the word STATISTICS.
a) how many ways can the letters in the word STATISTICS be arranged
b) how many ways are there of arranging the letters so all the S's are next to each other
c) what is the probability of all S's being next to each other
d) in how many ways are there of arranging the letters so all the vowels are next to each other
e) what is the probability of the word ending in T
f) Find the probability that the first three letters spell CAT.

if there is anyone that can help me i would really appreciate it. :smile::smile:


a) 10!/((2!)(3!)) - when there are letters the same, imagine they are distinguishable and see how many permutations you get. Then correct for the fact that actually they are indistinguishable
b)[7!/((3!)(2!))]*8 - consider permutations without the S and then there are 8 gaps to put them in. Alternatively do as in a) but considering the three S' as one object
c) a/b - Prob = number of outcomes wanted/ total no. of outcomes
d)[7!/(3!3!)] *3*8 - permutations without vowels then there are 8 gaps for vowels together and for each gap three distinguishablw rearrangements of the vowels


Will have to look at last two when not half asleep !
Reply 3
Avatar for Saliha I
Saliha I
OP
Original post by TeeEm
do you mean you cannot do any of this !!??

I can do some parts but just wanna see if im getting the answers right
Reply 4
Avatar for TeeEm
TeeEm
19
Original post by Saliha I
Hi
I'm really stuck on this questions on permutations. I can't remember the beginning of the question but all the different parts are related to finding arrangements of letters using the word STATISTICS.
a) how many ways can the letters in the word STATISTICS be arranged
b) how many ways are there of arranging the letters so all the S's are next to each other
c) what is the probability of all S's being next to each other
d) in how many ways are there of arranging the letters so all the vowels are next to each other
e) what is the probability of the word ending in T
f) Find the probability that the first three letters spell CAT.

if there is anyone that can help me i would really appreciate it. :smile::smile:


(a) 50400
(b) 3360
(c) 1/15
(d) 1/15
(e) 3/10
(f) 1/240

my answers in 90 seconds (hope no mistakes)
(d) 3360

Rest as per TeeEm
Reply 6
Avatar for Saliha I
Saliha I
OP
Original post by TeeEm
(a) 50400
(b) 3360
(c) 1/15
(d) 1/15
(e) 3/10
(f) 1/240

my answers in 90 seconds (hope no mistakes)

I got the same answers except for the last one I got 1/120
I did 1/10*1/9*3/8
Have I done anything wrong?
Reply 7
Avatar for Saliha I
Saliha I
OP
Original post by newblood
a) 10!/((2!)(3!)) - when there are letters the same, imagine they are distinguishable and see how many permutations you get. Then correct for the fact that actually they are indistinguishable
b)[7!/((3!)(2!))]*8 - consider permutations without the S and then there are 8 gaps to put them in. Alternatively do as in a) but considering the three S' as one object
c) a/b - Prob = number of outcomes wanted/ total no. of outcomes
d)[7!/(3!3!)] *3*8 - permutations without vowels then there are 8 gaps for vowels together and for each gap three distinguishablw rearrangements of the vowels


Will have to look at last two when not half asleep !


Thanks I think I understand now
Reply 8
Avatar for TeeEm
TeeEm
19
Original post by Saliha I
I got the same answers except for the last one I got 1/120
I did 1/10*1/9*3/8
Have I done anything wrong?


look at Q16 look at the link


http://madasmaths.com/archive/maths_booklets/statistics/combinations_and_permutations.pdf


hope this clears things out

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