A) 5
B) \[\frac{20}{7}\]
C) 4
D) \[\frac{10}{3}\]
Correct Answer: C
Solution :
Set\[A=\{{{a}_{1}},{{a}_{2}},.....,{{a}_{20}}\}\]has 20 distinct elements We have to select 5-element subset. \[\therefore \]Number of 5-element subsets \[{{=}^{20}}{{C}_{5}}\] According to question\[^{20}{{C}_{5}}=\left( ^{19}{{C}_{4}} \right)k\] \[\Rightarrow \]\[\frac{20!}{5!15!}=k.\left( \frac{19!}{4!15!} \right)\]\[\Rightarrow \]\[\frac{20}{5}=k\Rightarrow k=4\]
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