Q. A lady given a dinner party for six guest. The number of ways in which they may be selected from among ten friends, if two of the friends will not, attends the party together is
A) 112
B) 140
C) 164
D) None of these
Explanation
(b)
Number of friends to be invited=6
Let A, B be the friends who are not to attend the party together. Either none of A, B or one of A, B attend the party
$\therefore$ Number of ways of inviting friends
$= \ ^{10 - 2}C_{6} \times \ ^{2}C_{0} + \ ^{10 - 2}C_{5} \times \ ^{2}C_{1}$
$= 28 \times 1 + 56 \times 2 = 140$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.