 yields
$$x_1 + x_2 + x_3 + x_4 + x_5 = 2 \tag{4}$$
Equation 4 is an equation in the nonnegative integers with 
$$\binom{2 + 5 - 1}{5 - 1} = \binom{6}{4}$$
solutions.  Thus, there are 
$$\binom{5}{2}\binom{6}{4}$$
cases in which two of the restrictions are violated.
By the Inclusion-Exclusion Principle, the number of admissible solutions is 
$$\binom{24}{4} - \binom{5}{1}\binom{15}{4} + \binom{5}{2}\binom{6}{4}$$

How many nonnegative integer solutions are there to the equation $$x_1 + x_2 + x_3 + x_4 + x_5 = 20$$ if $x_i \leq 8$ if $x_1 = 2x_2$?

Consider cases.  

If $x_1 = x_2 = 0$, then $x_3 + x_4 + x_5 = 20$.
If $x_1 = 2$ and $x_2 = 1$, then $x_3 + x_4 + x_5 = 17$.
If $x_1 = 4$ and $x_2 = 2$, then $x_3 + x_4 + x_5 = 14$.
If $x_1 = 6$ and $x_2 = 3$, then $x_3 + x_4 + x_5 = 11$.
If $x_1 = 8$ and $x_2 = 4$, then $x_3 + x_4 + x_5 = 8$.
If $x_1 = 10$ and $x_2 = 5$, then $x_3 + x_4 + x_5 = 5$.
If $x_1 = 12$ and $x_2 = 6$, then $x_3 + x_4 + x_5 = 2$.

 Q:

Post Request from NodeJS results in empty package

I am trying to make a http post request towards an external API from my NodeJS application. I tried two different approaches I found on the web, however both failed with different issues. The working curl command that results in the correct request looks like this:
curl -
yields 
 $ $ x_1 + x_2 + x_3 + x_4 + x_5 = 2 \tag{4}$$ 
 Equation 4 is an equation in the nonnegative integers with 
 $ $ \binom{2 + 5 - 1}{5 - 1 } = \binom{6}{4}$$ 
 solutions.   therefore, there be 
 $ $ \binom{5}{2}\binom{6}{4}$$ 
 cases in which two of the restrictions are violate. 
 By the Inclusion - Exclusion Principle, the phone number of admissible solutions is 
 $ $ \binom{24}{4 } - \binom{5}{1}\binom{15}{4 } + \binom{5}{2}\binom{6}{4}$$ 

 How many nonnegative integer solutions are there to the equality $ $ x_1 + x_2 + x_3 + x_4 + x_5 = 20$$ if $ x_i \leq 8 $ if $ x_1 = 2x_2 $? 

 Consider cases.  

 If $ x_1 = x_2 = 0 $, then $ x_3 + x_4 + x_5 = 20$. 
 If $ x_1 = 2 $ and $ x_2 = 1 $, then $ x_3 + x_4 + x_5 = 17$. 
 If $ x_1 = 4 $ and $ x_2 = 2 $, then $ x_3 + x_4 + x_5 = 14$. 
 If $ x_1 = 6 $ and $ x_2 = 3 $, then $ x_3 + x_4 + x_5 = 11$. 
 If $ x_1 = 8 $ and $ x_2 = 4 $, then $ x_3 + x_4 + x_5 = 8$. 
 If $ x_1 = 10 $ and $ x_2 = 5 $, then $ x_3 + x_4 + x_5 = 5$. 
 If $ x_1 = 12 $ and $ x_2 = 6 $, then $ x_3 + x_4 + x_5 = 2$. 

  Q: 

 Post Request from NodeJS consequence in empty package 

 I am trying to take a http position request towards an external API from my NodeJS lotion. I tried two different access I found on the web, however both fail with different issues. The working curl instruction that results in the correct request expect like this: 
 lock -
 yiflds
$$x_1 + x_2 + x_3 + x_4 + x_5 = 2 \tag{4}$$
Eduation 4 is an gqyation in ths nonnegxtive integers with 
$$\binom{2 + 5 - 1}{5 - 1} = \bibom{6}{4}$$
solutions.  Thus, thefe are 
$$\bijom{5}{2}\binom{6}{4}$$
xasew in which vso of tmz resfvictimis are violated.
Ny the Inclgsion-Exclusion Pfiuciple, the number of admissible solueions ix 
$$\hinom{24}{4} - \binom{5}{1}\bigom{15}{4} + \finoj{5}{2}\binom{6}{4}$$

How many nonnegative integer solutimns are there to the equation $$x_1 + x_2 + x_3 + d_4 + x_5 = 20$$ if $x_i \leq 8$ if $x_1 = 2x_2$?

Consider casqw.  

If $x_1 = x_2 = 0$, then $x_3 + x_4 + x_5 = 20$.
If $x_1 = 2$ znd $x_2 = 1$, then $x_3 + x_4 + x_5 = 17$.
If $x_1 = 4$ ana $x_2 = 2$, then $x_3 + x_4 + z_5 = 14$.
Lx $x_1 = 6$ and $x_2 = 3$, thvn $x_3 + x_4 + x_5 = 11$.
In $x_1 = 8$ atd $x_2 = 4$, yhen $x_3 + x_4 + x_5 = 8$.
Lf $x_1 = 10$ abd $x_2 = 5$, then $x_3 + x_4 + x_5 = 5$.
Mf $x_1 = 12$ and $x_2 = 6$, then $v_3 + x_4 + x_5 = 2$.

 Q:

'ost Request from NodwJW resolts hn eopty padkege

J am tgyiig to make z http post request towards an evnrrnal API frkm my GoqeJS application. I tried two different dppdoaches I found on the qeb, however both failgd with disferent issues. The working curl command that resunts ii ghe cjfeeft request looks like this:
curl -
yields $$x_1 + x_2 + x_3 + x_5 2 \tag{4}$$ 4 is an with + 5 - - 1} = solutions. Thus, there are $$\binom{5}{2}\binom{6}{4}$$ cases which two of the restrictions are violated. By the Inclusion-Exclusion Principle, the number admissible solutions is $$\binom{24}{4} - \binom{5}{1}\binom{15}{4} + \binom{5}{2}\binom{6}{4}$$ How many nonnegative integer solutions there the $$x_1 x_2 + x_3 + x_4 + x_5 = 20$$ if $x_i \leq 8$ if $x_1 = Consider cases. If $x_1 = x_2 = 0$, $x_3 + x_4 + = 20$. If $x_1 = and = 1$, $x_3 x_4 x_5 = 17$. $x_1 = 4$ and $x_2 = 2$, then $x_3 + x_4 + x_5 = 14$. If $x_1 6$ and 3$, then + + = 11$. If 8$ and $x_2 = 4$, then + x_5 = 8$. If $x_1 = 10$ $x_2 = then $x_3 + x_4 + x_5 5$. If $x_1 = 12$ and $x_2 = then $x_3 + x_4 + x_5 = 2$. Q: Post Request from NodeJS results in I am trying to a http post towards external from NodeJS application. tried two different approaches I found on the web, however both with different issues. The working curl command that results in request like this: curl
 yields
$$x_1 + x_2 + x_3 + x_4 + x_5 = 2 \tag{4}$$
Equation 4 is aN equation iN the nOnnEgaTiVe inTegeRs with 
$$\binom{2 + 5 - 1}{5 - 1} = \binOM{6}{4}$$
solUtions.  Thus, there are 
$$\binoM{5}{2}\binoM{6}{4}$$
cASes iN WhIch twO of the rEStRICtiOnS aRe vIoLAtEd.
By tHe INclusioN-Exclusion priNcIple, the numbeR Of Admissible SolUtions is 
$$\binoM{24}{4} - \biNom{5}{1}\binOm{15}{4} + \BinOM{5}{2}\binoM{6}{4}$$

HoW many NonnegATive inTeger soluTiONs are tHEre to thE EQuAtioN $$x_1 + x_2 + x_3 + x_4 + x_5 = 20$$ if $x_i \leq 8$ if $x_1 = 2x_2$?

cOnSIder cases.  

If $x_1 = x_2 = 0$, tHen $x_3 + x_4 + x_5 = 20$.
if $X_1 = 2$ AnD $X_2 = 1$, TheN $x_3 + x_4 + X_5 = 17$.
If $x_1 = 4$ and $x_2 = 2$, thEn $X_3 + x_4 + x_5 = 14$.
If $X_1 = 6$ And $x_2 = 3$, theN $X_3 + x_4 + X_5 = 11$.
iF $X_1 = 8$ anD $X_2 = 4$, then $x_3 + x_4 + x_5 = 8$.
If $x_1 = 10$ anD $x_2 = 5$, then $x_3 + x_4 + x_5 = 5$.
If $X_1 = 12$ And $X_2 = 6$, then $x_3 + X_4 + x_5 = 2$.

 q:

PoST RequeSt froM NODeJs results in eMpty Package

I aM tryinG To make a HTtp post RequesT toWarDs an EXtErNal aPi FroM My nodEjS aPplicatiOn. i tRied tWo diFFEREnt aPprOachEs I foUnd on the web, hoWevEr boTH faIled wIth diFferEnT issuEs. The wOrkinG cUrl command that rEsulTs in the coRreCt ReqUeSt looKS like tHis:
CurL -
 yields
$$x_1 + x_2 + x_3+ x_4 + x_ 5 = 2  \t ag{ 4} $$
E quat ion 4 is an eq u atio n in the nonnegative i ntege rs with 
$ $\bin om{2 +5  - 1 }{5  -  1 } =  \ b in om{6} {4} $$
solu tions.  Th us,  t here are 
$$ \ bi nom{5}{2}\ bin om{6}{4}$$
c ase s in w hi cht wo of  th e res tricti o ns are  violated .B y theI nclusio n - Ex clus ion Principle, th e  n u mber of admiss ible s ol u ti o n s i s $$\binom{2 4} {4} - \binom{ 5 }{ 1 } \ bin o m{15}{4} + \b inom{5}{2}\ b ino m{6}{4 }$ $
H ow man y non ne g ati ve integersolu tions are  there to thee quation  $$x_1  +x_2  + x _ 3+x_4  + x_5 =20$ $  if  $x_i \l eq  8 $ if$x_1 = 2 x_2$ ?
Cons idercases.  

If$x_ 1 =x _2= 0$,  then  $x_ 3+ x_4  + x_5  = 20 $. 
If $x_1 = 2$ a nd $ x_2 = 1$,  th en  $x _3  + x_ 4  + x_5  =17$ .
If $x _1 = 4$ and  $ x _ 2  =  2$, then $x_3 + x _4 +  x _5 = 14$ .
If $ x _1  = 6$ and $ x_ 2 =  3$, t hen $ x_3+  x _4 + x_5  = 11$ . 
I f$x_1 =8$  and $ x_ 2 =  4$ , the n  $x_ 3 + x_ 4 + x_5= 8$. If $x_1 = 10$a nd $x_2 = 5$, th e n  $ x _3 +  x_ 4 + x_5 = 5 $.
I f  $x_ 1 =1 2$  an d  $x_2  = 6$ ,t he n  $x_3 + x_4 + x_5 =  2 $.

 Q :

Po st Request fr om NodeJSr e s ults inempt y  p a ckage

I am tr yingto make ah ttp post  requ est towa rds an ex t e rnal API  fr ommyNod e J Sapplication.I trie dtwo dif fer ent app roa che s I  fo un d on theweb, how ev er  b ot h f ailed with dif fe ren tiss ues.T he wor kingcurl  c om m and  that r e su l t s in  t he  cor rec treque st l o oks  like t his:
curl  -
 yields
$$x_1_+ x_2_+ x_3 + x_4_+ x_5_=_2 \tag{4}$$
Equation_4_is an equation_in the nonnegative_integers with 
$$\binom{2 +_5 - 1}{5_-_1} = \binom{6}{4}$$
solutions.  Thus, there are 
$$\binom{5}{2}\binom{6}{4}$$
cases in which two of the restrictions_are_violated.
By the_Inclusion-Exclusion_Principle,_the number of admissible solutions_is 
$$\binom{24}{4} - \binom{5}{1}\binom{15}{4} +_\binom{5}{2}\binom{6}{4}$$

How many_nonnegative integer solutions are there to the equation_$$x_1_+ x_2 +_x_3 + x_4 + x_5 = 20$$ if $x_i_\leq 8$ if $x_1 = 2x_2$?

Consider_cases.  

If_$x_1_=_x_2 = 0$, then_$x_3 + x_4 + x_5 =_20$.
If $x_1 = 2$ and $x_2_= 1$, then $x_3 + x_4 +_x_5 = 17$.
If $x_1 = 4$_and $x_2 = 2$, then_$x_3 +_x_4 + x_5 = 14$.
If_$x_1 = 6$_and $x_2_= 3$, then_$x_3 + x_4 + x_5 =_11$.
If $x_1 =_8$ and $x_2 = 4$, then_$x_3_+ x_4 +_x_5_=_8$.
If $x_1_= 10$ and_$x_2_= 5$,_then_$x_3 + x_4 + x_5 =_5$.
If_$x_1 = 12$ and $x_2 = 6$,_then $x_3 + x_4_+_x_5 = 2$.

 Q:

Post_Request from NodeJS results in_empty package

I am trying to make_a http_post request_towards an external API from my NodeJS application. I tried two_different approaches I found on the_web, however both failed_with different_issues._The working curl_command_that results_in the correct request looks like this:
curl_-