A) \[^{56}{{C}_{3}}\]
B) \[^{56}{{C}_{4}}\]
C) \[^{55}{{C}_{4}}\]
D) \[^{55}{{C}_{3}}\]
Correct Answer: B
Solution :
\[{{\,}^{50}}{{C}_{4}}+\,\left( ^{50}{{C}_{3}}{{+}^{51}}{{C}_{3}}+{{\,}^{52}}{{C}_{3}}+......{{\,}^{55}}{{C}_{3}} \right)\]. Taking first two terms together and adding them and following the same pattern, we get\[{{\,}^{56}}{{C}_{4}}\], \[[As\,{{\,}^{n}}{{C}_{r}}+{{\,}^{n}}{{C}_{r-1}}={{\,}^{n+1}}{{C}_{r}}]\].
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