Question

${}^{14}{C}_7+\sum _{i=1}^3{}^{17-i}{C}_6=$

• A. ${}^{16}{C}_7$
• B. ${}^{17}{C}_7^{}$
• C. ${}^{17}{C}_8^{}$
• D. ${}^{16}{C}_8^{}$

Answer 1

Answer: (B)

$14C_7+\sum _{i=1}^3{}^{17-i}{C}_6^{}$
${}^{14}{C}_7+{}^{14}{C}_6^{}+{}^{15}{C}_6^{}+{}^{16}{C}_6^{}$
$={}^{15}{C}_7^{}+{}^{15}{C}_6^{}+{}^{16}{C}_6^{}$
$={}^{16}{C}_7^{}+{}^{16}{C}_6^{}={}^{17}{C}_7^{}$