Evaluate:

We know that:

${ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=\frac{n !}{(n-r) ! \times r !}$

$\Rightarrow{ }^{16} \mathrm{C}_{13}=\frac{16 !}{(16-13) ! \times 13 !}$

$\Rightarrow{ }^{16} \mathrm{C}_{13}=\frac{16 !}{3 ! \times 13 !}$

$\Rightarrow{ }^{16} \mathrm{C}_{13}=\frac{16 \times 15 \times 14 \times 13 !}{3 ! \times 13 !}$

$\Rightarrow{ }^{16} \mathrm{C}_{13}=\frac{16 \times 15 \times 14}{3 !}$

$\Rightarrow{ }^{16} \mathrm{C}_{13}=\frac{16 \times 15 \times 14}{3 \times 2 \times 1}$

$\Rightarrow{ }^{16} C_{13}=\frac{3360}{6}$

$\Rightarrow{ }^{16} \mathrm{C}_{13}=560$

Ans: ${ }^{16} \mathrm{C}_{13}=560$