A) 100
B) 200
C) 50
D) 400
Correct Answer: A
Solution :
\[\sum\limits_{i=1}^{20}{{}}{{\left( \frac{^{20}{{C}_{i-1}}}{^{21}{{C}_{i}}} \right)}^{3}}\,\,=\,\,{{\sum\limits_{i=1}^{20}{\left( \frac{i}{21} \right)}}^{3}}\,=\,\frac{1}{{{(21)}^{3}}}{{\left( \frac{20.21}{2} \right)}^{2}}\] \[\frac{100}{21}\,=\,\frac{k}{21}\] \[\therefore \text{ }k=100\]
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