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
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
Solution:
(c) ${ }^{12} C_{8}-{ }^{10} C_{6}$
A host lady can invite 8 out of 12 people in
∴ Number of ways = 12C8 − 10C6