The number of values in set of values of r for which ${ }^{23}{\mathrm{C}}_{\mathrm{r}}+2{\cdot }^{23}{\mathrm{C}}_{\mathrm{r}+1}{+}^{23}{\mathrm{C}}_{\mathrm{r}+2}{\ge }^{25}{\mathrm{C}}_{15}\mathrm{ }$is ______.

${ }^{23}{\mathrm{C}}_{\mathrm{r}}+2{\cdot }^{23}{\mathrm{C}}_{\mathrm{r}+1}{+}^{23}{\mathrm{C}}_{\mathrm{r}+2}{=}^{24}{\mathrm{C}}_{\mathrm{r}+1}{+}^{24}{\mathrm{C}}_{\mathrm{r}+2}{=}^{25}{\mathrm{C}}_{\mathrm{r}+2}{\ge }^{25}{\mathrm{C}}_{15}$
Therefore, (r + 2) can be 10, 11,12 ,13,14 and 15.
So there are 6 elements.