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Quick math

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#1
HardStuckGold

i know i shouldnt be posting this on a vlr thread but rq question please if someone could do this;

How many different arrangements are there of the word ACTIVATED if the 2 A's must be AT LEAST 5 numbers away from each other

please ty ily if u can solve

#2
charizard_123
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at least 6

#3
Brimstan
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over 1

#4
equinoxyy
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im bad at math, but why tf would your teacher gave u this question?

#10
HardStuckGold
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its cambridge as maths questions this year im pre sure i fucked it up ;-;

#5
andrewdamf
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69

#6
number1_ScreaM_fan
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wtf is this question

#7
qwertyuiopasdfghjklzxcvbn
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isn't it 0

#8
number1_ScreaM_fan
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i counted 5
edit ignore i made mistake

#9
Afterburnz
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Im smol brain sorry

#11
boberto1108
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f

#12
annoybrocc02
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it's been a while since i had permutations class, please correct me if i'm wrong
A C T I V A T E D
if 2 A's are separated by 5 letters then the word would be in the form: A (5 random letters) A (2 random letters)
If there were no repeated letters, the number of permutations would be 7! for 7 blank spaces
Since T is present twice, we divide it by 2!, which would mean number of permutations = 7!/2! = 2520

Similarly, the two A's can be separated by 6 and 7 letters too, total permutations = 2520 * 3 = 7560

forgive me if i am wrong i tried :)

#21
M0K1
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you forgot to multiply with 3! on the 5 letter gap coz the 2 letters and the object can also be arranged
for 6 letter gap it should be multiplied with 2!

#23
PRLV
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why would that make any difference, this is not combinations, order dosent matter, what matter is there are 7 blank spaces and 7 letters to fill it aka 7! arrangements

#26
M0K1
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it depends on the method you use if you make the [A----A] an object you will have to arrange it, if you do it without object then it doesn't

#13
horse69
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a- - - - - a- -
a- - - - - - a -
a- - - - - - - a
-a- - - - - a -
-a- - - - - - a
— — a - - - - - a
the dashes are 7! for each of them, and there are 6 arrangements of ‘a’ , so 7! X 6. but there are two ‘t’ in activated, so divide the answer by 2 ( im not sure) so answer is 3 * 7!

#14
M0K1
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https://www.quora.com/Given-the-word-STAPLE-how-many-different-arrangements-are-there-of-the-letters-such-that-A-and-E-are-separated-by-at-least-one-letter
this might help you
note in your case both letters are the same so divide by 2!

#15
horse69
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activated has two Ts so its different

#16
M0K1
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yeah, but the logic used here is rather than calculating specifically we find the ones that don't agree with our conditions and subtract them from all possible outcomes

#18
HardStuckGold
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but itll be too hard cus u need to consider A together, A 1 apart, A 2 apart, etc... wouldnt it be simpler to just calculate 5 6 7 ?

#20
M0K1
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yeah you can do that but there's gotta be an easy way, I'll let you know if I find it

#17
1phnxe
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There is literally zero application for this question in the real world.

#19
M0K1
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if you understand the basics it can be used in programming, this question is for strengthening basics

#24
Zorontom
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Well permutation combination has lots of applications in data management

#22
PRLV
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ACTIVATED has 9 letters
we need to arrange 2 A's so not counting A, there are 7 letters and 7! ways to arrange those.
However the letter T is repeteated twice, so we divide 7!/2!
Question says atleast 5, so we multiple 7!/2! with 3 for all arangements for 5 letter gap, 6 letter gap and 7 letter gap

thus answer is 7!/2! * 3

#25
Noodle
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25200

#27
SAMPV6
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I love how most serious answers in this thread come from India flags, y'all so smart

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