A) \[5(n-3)\]
B) \[5(n-2)\]
C) \[5n\]
D) \[5(2n-9)\]
Correct Answer: B
Solution :
\[\frac{^{n}{{C}_{r}}}{^{n}{{C}_{r-1}}}=\frac{r.\left| \!{\nderline {\, n \,}} \right. }{\left| \!{\nderline {\, r \,}} \right. .\left| \!{\nderline {\, n-r \,}} \right. }\cdot \frac{\left| \!{\nderline {\, r-1 \,}} \right. \left| \!{\nderline {\, n-r \,}} \right. +1}{\left| \!{\nderline {\, n \,}} \right. }=\frac{\left| \!{\nderline {\, n-r \,}} \right. +1}{\left| \!{\nderline {\, n-r \,}} \right. }\] \[=\frac{\left| \!{\nderline {\, n-r \,}} \right. +1}{\left| \!{\nderline {\, n-r \,}} \right. }=n-r+1\] \[\therefore \]\[\sum\limits_{r=1}^{5}{=}n+(n-1)+(n-2)+(n-3)+(n-4)\] \[=5n-10=5(n-2)\]
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