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in Combinatorics and Mathematical Induction by (49.1k points)
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The number of ways in which a host lady invite 8 people 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) 11C7 + 10C8 

(c) 12C810C6

(d) 10C6 + 2!

1 Answer

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Best answer

(c) 12C810C6

Number of way of selecting 8 people from 12 in 12C8 

∴ out of remaining people 8 can attend in 10C8 

The number of ways in which two of them do not attend together = 12C810C6

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