Find the number of 5-lists of the form (x1, x2, x3, x4, x5), where each xi
is a nonnegative integer and x1 + x2 + x3 + x4 + 3x5 = 12.
#Combinatorics Help
autumn wedge
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Find the number of 5-lists of the form (x1, x2, x3, x4, x5), where each xi
is a ...
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autumn wedge
So far what i did is substitute x5 for 0,1,2,3,4 and create new equations
which are
a + b + c + d = 12
a + b + c + d = 9
a + b + c + d = 6
a + b + c + d = 3
a + b + c + d = 0
where a is x1, b is x2 and so on
now the problem is getting the amount of probabilities for each
the last one is obviously 1
but then the rest is terrifying
for the penuultimate equation i got 19
bc
if all were 1 except for one value
itd be 6 ways
there are 12 ways to arrange 2 and 1
and 1 way to arrange 3
6 = 5 + 1
= 4 + 2
= 3 + 3
autumn wedge
6 = 5 + 1
= 4 + 2
= 3 + 3
btw this is for middle equation
autumn wedge
6 = 5 + 1
= 4 + 2
= 3 + 3
can be broken into 4 + 1 + 1, 3 + 2 + 1,
autumn wedge
6 = 5 + 1
= 4 + 2
= 3 + 3
and 2 + 2
this can be broken down into
3 + 1 + 1 + 1, 2 + 2 + 1 + 1,
AND U HAVE TO FIND THE POSSIBILITIES OF ALL OF THEM
AND THEN REPEAT THIS AGAIN
FOR 2 MORE TIMES
BUT MORE COMPLEX 😭
autumn wedge
6 = 5 + 1
= 4 + 2
= 3 + 3
thats 12 + 12 + 6
autumn wedge
can be broken into 4 + 1 + 1, 3 + 2 + 1,
12 + 36
autumn wedge
3 + 1 + 1 + 1, 2 + 2 + 1 + 1,
6 + 6?
i can't do this again and again 😭
wait is the answer 4^4?
love how im talking to myself
autumn wedge
wait is the answer 4^4?
BRUH
DID ALL THAT FOR ME TO RELAIZE
BTW THE WAY I GOT IS
N^R
in order matter no matter repitiion no repittion table thingy
autumn wedge
and nvm
peak moss
you can start by considering the possibilities for x5 (0 to 4) and then just stars and bars the rest
@autumn wedge
sorry i thought someone already helped you from the message count lol
autumn wedge
you can start by considering the possibilities for x5 (0 to 4) and then just sta...
uhhhhh
.....
peak moss
wha
autumn wedge
uh
peak moss
no its like uhh
i want 5 scoops of icecream and there are 3 flavours avaliable
how many different combinations of flavours can i get
and then you do
ooooo||
and then like uh
| separates the number of flavour of one kind
so oo|o|oo means tehres 2 of flavour 1, 1 of flavour 2, 2 of flavour 3
peak moss
no its like uhh
i want 5 scoops of icecream and there are 3 flavours avaliable
and gives you the number if ways you can do that
familiar or nah
autumn wedge
autumn wedge
familiar or nah
ye
autumn wedge
this right
peak moss
yea