The number of ways in which a host lady invite 8 people for a party of

1.	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) 12C8 – 10C6(d) 10C6 + 2!
Answer» (c) ¹²C₈ – ¹⁰C₆ 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 = ¹²C₈ – ¹⁰C₆

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) 12C8 – 10C6(d) 10C6 + 2!

Answer»

(c) ¹²C₈ – ¹⁰C₆

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 = ¹²C₈ – ¹⁰C₆