Evaluate:

We know that:

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

$\Rightarrow{ }^{90} \mathrm{C}_{88}=\frac{90 !}{(90-88) ! \times 88 !}$

$\Rightarrow{ }^{90} \mathrm{C}_{88}=\frac{90 !}{2 ! \times 88 !}$

$\Rightarrow{ }^{90} \mathrm{C}_{88}=\frac{90 \times 89 \times 88 !}{2 ! \times 88 !}$

$\Rightarrow{ }^{90} \mathrm{C}_{88}=\frac{90 \times 89}{2 !}$

$\Rightarrow{ }^{90} \mathrm{C}_{88}=\frac{90 \times 89}{2 \times 1}$

$\Rightarrow{ }^{90} \mathrm{C}_{88}=\frac{8010}{2}$

$\Rightarrow{ }^{90} \mathrm{C}_{88}=4005$

Ans: $\Rightarrow{ }^{90} \mathrm{C}_{88}=4005$