Question

The value of ${}^{16}{C}_9+{}^{16}{C}_{10}-{}^{16}{C}_6-{}^{16}{C}_7$ is

• A. 0
• B. 1
• C. ${}^{17}{C}_{10}$
• D. ${}^{17}{C}_3$

Answer 1

Answer: (A)

${}^{16}{C}_9+{}^{16}{C}_{10^{-}}{}^{16}{C}_{6^{-}}{}^{16}{C}_7$
$={}^{16}{C}_9+{}^{16}{C}_{10^{-}}{}^{16}{C}_{10^{-}}{}^{16}{C}_9=0$
$\left(\because {}^n{C}_r={}^n{C}_{(n-r)}\right)$