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 12C8">12C812C8 ways. Two out of these 12 people do not want to attend the party together.

∴ Number of ways = 12C8 − 10C6

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