Question

The value of ${}^{10}{C}_4{+}^9{C}_4{+}^8{C}_4+...{+}^5{C}_4$ is-------------

• A. ${}^{11}{C}_5$
• B. ${}^{11}{C}_4$
• C. ${}^{11}{C}_7$
• D. ${}^{11}{C}_5-1$

Answer 1

The correct option is D ${}^{11}{C}_5-1$

We know that,

${}^n{C}_r{+}^n{C}_{r-1}{=}^{n+1}{C}_r$

Since,

${\Rightarrow }^{10}{C}_4{+}^9{C}_4{+}^8{C}_4{+}^7{C}_4{+}^6{C}_4{+}^5{C}_4{+}^5{C}_5-1$

${\Rightarrow }^{10}{C}_4{+}^9{C}_4{+}^8{C}_4{+}^7{C}_4{+}^6{C}_4{+}^6{C}_5-1$

${\Rightarrow }^{11}{C}_5-1$

Hence, this is the answer.