Question

The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is

• A. $2\times {}^{11}{C}_7+{}^{10}{C}_8$
• B. ${}^{10}{C}_8+{}^{11}{C}_7$
• C. ${}^{12}{C}_8+{}^{10}{C}_6$
• D. $\text{None of these}$

Answer 1

Answer: (C)

(${}^{12}{C}_8+{}^{10}{C}_6$)

A host lady can invite 8 out of 12 people in ${}^{12}{C}_8$ ways. Two out of these 12 people do not want to attend the party together.

$\therefore$ Number of ways $={}^{12}{C}_8-{}^{10}{C}_6$