Question

Then value of?

${\sum }_{r=0}^3{C}_r{(}^5{\text{C}}_{r+1}-{}^4{\text{C}}_r)$ equals

• A. 210
• B. 220
• C. 120
• D. 110

Answer 1

Answer: (B)

220

${\sum }_{r=0}^3{C}_r{}^4{C}_{r+1}={}^8{C}_0\cdot {}^4{C}_1+{}^8{C}_1\cdot {}^4{C}_2+{}^8{C}_2\cdot {}^4{C}_3+{}^8{C}_3\cdot {}^4{C}_4$

$={}^8{C}_0\cdot {}^4{C}_3+{}^8{C}_1\cdot {}^4{C}_2+{}^8{C}_2\cdot {}^4{C}_1+{}^8{C}_3\cdot {}^4{C}_0$

$={}^{12}{C}_3$

$=220$