Evaluate:

Question:

Evaluate: 

${ }^{20} \mathrm{C}_{4}$

Solution:

We know that:

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

$\Rightarrow{ }^{20} \mathrm{C}_{4}=\frac{20 !}{(20-4) ! \times 4 !}$

$\Rightarrow{ }^{20} \mathrm{C}_{4}=\frac{20 !}{16 ! \times 4 !}$

$\Rightarrow{ }^{20} \mathrm{C}_{4}=\frac{20 \times 19 \times 18 \times 17 \times 16 !}{16 ! \times 4 !}$

$\Rightarrow{ }^{20} \mathrm{C}_{4}=\frac{20 \times 19 \times 18 \times 17}{4 !}$

$\Rightarrow{ }^{20} \mathrm{C}_{4}=\frac{20 \times 19 \times 18 \times 17}{4 \times 3 \times 2 \times 1}$

$\Rightarrow{ }^{20} \mathrm{C}_{4}=\frac{116280}{24}$

$\Rightarrow{ }^{20} \mathrm{C}_{4}=4845$

Ans: ${ }^{20} \mathrm{C}_{4}=4845$

 

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