Wardrobe code

Lucia has a lock on her wardrobe that opens with a 4-digit code (such as 0000, 0089, or 9123).
Lucia forgot her code. But she knows that the sum of all four digits of her code is 4. How many such codes are there?

Correct answer:

n =  34

Step-by-step explanation:

$$\begin{gathered} s=4 \\ s=4=4+0=3+1=2+2=1+1+1+1=1+1+2 \\ {x}_1=0004 \\ {x}_2=0013 \\ {x}_3=0022 \\ {x}_4=0031 \\ {x}_5=0040 \\ {x}_6=0103 \\ {x}_7=0112 \\ {x}_8=0121 \\ {x}_9=0130 \\ {x}_{10}=0202 \\ {x}_{11}=0211 \\ {x}_{12}=0220 \\ {x}_{13}=0301 \\ {x}_{14}=0310 \\ {x}_{15}=0400 \\ {x}_{16}=1003 \\ {x}_{17}=1012 \\ {x}_{18}=1021 \\ {x}_{19}=1030 \\ {x}_{20}=1102 \\ {x}_{21}=1111 \\ {x}_{22}=1120 \\ {x}_{23}=1201 \\ {x}_{24}=1210 \\ {x}_{25}=1300 \\ {x}_{26}=2002 \\ {x}_{27}=2011 \\ {x}_{28}=2020 \\ {x}_{29}=2101 \\ {x}_{30}=2110 \\ {x}_{31}=2200 \\ {x}_{32}=3001 \\ {x}_{33}=3010 \\ {x}_{34}=3100 \\ {x}_{35}=4000 \\ n=34 \end{gathered}$$

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