Question

A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is

• A. $112$
• B. $140$
• C. $164$
• D. none of these

Answer 1

Answer: (B)

$140$

Answer 2

Reqd. no of ways $=\,^{10}C_{6}-\,^{8}C_{4}=210-70 =140$ [$\because$ no. of ways in which two of the friends will attend the party $=\,^{8}C_{4}]$