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 × ¹¹C₇ + ¹⁰C₈
(b) ¹⁰C₈ + ¹¹C₇
(c) ¹²C₈ − ¹⁰C₆
(d) none of these

Answer 1

(c) ¹²C₈ − ¹⁰C₆

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.
∴ Number of ways = ¹²C₈ − ¹⁰C₆