Mathematics - Permutation & Combination Question with Solution | TestHub

Set $A=\left\{a_1,a_2,\dots ..,a_{20}\right\}$ has 20 distinct elements. We have to select 5-element subset. $\therefore$ Number of 5-element subsets $={}^{20}{\mathrm{C}}_5$ According to question $$\begin{array}{rl}& {}^{20}{\mathrm{C}}_5=({}^{19}{\mathrm{C}}_4\cdot k\\ & \Rightarrow \frac{20!}{5!15!}=k\cdot \left(\frac{19!}{4!15!}\right)\\ & \Rightarrow \frac{20}{5}=k\Rightarrow k=4\end{array}$$