Q. 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 attent the party together, is
A) 112
B) 140
C) 164
D) None of these
Explanation
(b)
There are two cases arise
Case I They do not invite the particular friend
$= {\ ^{8}C}_{6} = 28$
Case II They invite one particular friend
$= {\ ^{8}C}_{5} \times {\ ^{2}C}_{1} = 112$
$\therefore$ Required number of ways =28+112=140
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.