help pls (permutation and combination)
#help pls (permutation and combination)
waxen panther
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help pls (permutation and combination)
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analog sigil
help pls (permutation and combination)
well, let's start with part a.
we know that we can treat the smart watches as one block, and that the tablets shouldn't be next to each other.
then, do complimentary counting with the tablets, i.e. you count the total amount of arrangements where the tablets are together and subtract it from the total arrangements possible.
then just multiply the latter by the amount of permutations for the smart watches
if you need me to explain the intuition, you can ping me
analog sigil
7p3 x 6!
wel, you can’t just give me some calculation without intuition
why is that the case?
waxen panther
t1 p1 t2 p2 t3 p3 t4 p4 t5 p5 t6 p6 w1 w2 w3 t7
7 option out of 3 must fill in tablet
?
@analog sigil
waxen panther
t means tablet p means phone and w means watches
Watches must to together so w1 w2 w3 together
analog sigil
Watches must to together so w1 w2 w3 together
yes
brisk charm
finding arrangements with tablets next to each other is going to be a bit taxing with 3 tablets. it would be easier to imagine first arranging the watches (as 1 block of 3) and phones, then inserting the tablets between them. you can imagine empty slots between them (and on the outside), and then you want to permute the tablets among these slots
analog sigil
but put them into one W block
waxen panther
Oh
analog sigil
like T1 T2 T3 S1...S5 and W
waxen panther
t1 p1 t2 p2 t3 p3 t4 p4 t5 p5 t6 p6 w1-3 t7
analog sigil
no need o write it out
analog sigil
t1 p1 t2 p2 t3 p3 t4 p4 t5 p5 t6 p6 w1-3 t7
more than one possibility for them to not be next to each other
my point was to use complimentary counting
waxen panther
What is that
analog sigil
to count the permutations where tablets are together
then subtract the total amount of permutation from it
waxen panther
How to count?
analog sigil
How to count?
put them together
waxen panther
11! / 3! x 7!
analog sigil
force them into a pair or triplet
waxen panther
?
analog sigil
one second
analog sigil
11! / 3! x 7!
why?
waxen panther
11 items
Divide by 3 identical item (watches)
Then
Wait
Sorry
I'm confused by my own stuff😅
analog sigil
...
analog sigil
we know that we can treat the smart watches as one block, and that the tablets s...
refer back to this, please
read the whole thing carefully
brisk charm
finding arrangements with tablets next to each other is going to be a bit taxing...
||for the phones and watches, you can permute them 3!*6! ways. then there are 7p3 ways you can insert the tablets between them (keeping the 3 watches together)||
brisk charm
basically you permute the phones and watches, p1, p2, p3, p4, p5 and w1w2w3. so that's 6 elements. but also you can permute w1, w2, w3. and then you permute the tablets amongst the empty spaces because you can have at most one tablet in each one
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@waxen panther