Question

The Value of ${}^{14}{C}_2+{}^{14}{C}_3+{}^{14}{C}_4+.....+{}^{14}{C}_{14}$ is

• A. 2¹⁴-14
• B. 2¹⁴-15
• C. an odd number ≠2¹⁴-15
• D. an even number ≠2¹⁴-14

Answer 1

The correct option is B

2¹⁴-15

$C_0+C_1+C_2+......+C_n=2^n$

${}^{14}{C}_2+{}^{14}{C}_3+{}^{14}{C}_4+.....{}^{14}{C}_{14}=2^{14}-({}^{14}{C}_0+{}^{14}{C}_1)=2^{14}-15$