A) 210
B) 220
C) 120
D) 110
Correct Answer: B
Solution :
\[\sum\limits_{r=\,0}^{3}{{}^{8}{{C}_{r}}}{}^{4}{{C}_{r+1}}={}^{8}{{C}_{0}}\cdot {}^{4}{{C}_{1}}+{}^{8}{{C}_{1}}\cdot {}^{4}{{C}_{2}}+{}^{8}{{C}_{2}}\cdot {}^{4}{{C}_{3}}+{}^{8}{{C}_{3}}\cdot {}^{4}{{C}_{4}}\] \[={}^{8}{{C}_{0}}\cdot {}^{4}{{C}_{3}}+{}^{8}{{C}_{1}}\cdot {}^{4}{{C}_{2}}+{}^{8}{{C}_{2}}\cdot {}^{4}{{C}_{1}}+{}^{8}{{C}_{3}}\cdot {}^{4}{{C}_{0}}={}^{12}{{C}_{3}}=220\]
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