Which of the following is /are true

The number of distinct terms in the expansion of $\left(1+2\mathrm{x}+4{\mathrm{x}}^3+6{\mathrm{x}}^5\right){\left(1+{\mathrm{x}}^5\right)}^{20}\text{ is }64$

The number of rational terms in the expansion of $(\sqrt{2}+\sqrt[3]{3}+\sqrt[6]{5}{)}^{10}\text{ is }3$

The greatest integer less than or equal to $(\sqrt{3}+1{)}^6\text{ is }415$

The number of different terms in the expansion of $(1+\mathrm{x}{)}^{2009}+{\left(1+{\mathrm{x}}^2\right)}^{2008}+{\left(1+{\mathrm{x}}^3\right)}^{2007}\text{ is }4017$