Question

The number of ways in which a host lady can invite for a party of $8$ out of $12$ people 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. $Noneofthese$

Answer 1

The correct option is C ${}^{12}{C}_8{-}^{10}{C}_6$

Total no, of ways so that two ladies are not attending at the same=Total no, of ways-No, of ways when both ladies are together.

${=}^{12}{C}_8{-}^{10}{C}_6$

Hence,

Option $C$ is correct answer.