Fractional part of the number 4 2022 15 is equal to

Given that $\frac{4^{2022}}{15}$

We know that ${\left(a+x\right)}^n={}^{n}C_0{a}^n{x}^0+{}^{n}C_1{a}^{n-1}{x}^1+.....+{}^{n}C_n{a}^0{x}^n$

$\Rightarrow \frac{4^{2022}}{15}=\frac{{16}^{1011}}{15}=\frac{{\left(15+1\right)}^{1011}}{15}$

$=\frac{{}^{1011}C_0{\left(15\right)}^{1011}+{}^{1011}C_1{\left(15\right)}^{1010}+.....+{}^{1011}C_{1011}{\left(15\right)}^0}{15}$

$=\frac{{}^{1011}C_0{\left(15\right)}^{1011}+{}^{1011}C_1{\left(15\right)}^{1010}+.....+{}^{1011}C_{1010}{\left(15\right)}^1}{15}+\frac{1}{15}$

$\therefore$ Fractional part of$\frac{4^{2022}}{15}=\frac{1}{15}$

Hence this is the required option.