Q. There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls, one in each box, could be placed such that a ball does not go to box of its own colour, is
A) 8
B) 7
C) 9
D) None of these
Explanation
(c)
The number of ways in which four different balls can be placed in four different boxes
$=^{4}C_{1} +^{3}C_{1} +^{2}C_{1} +^{1}C_{1}$
$= 4 + 3 + 2 + 1 = 10$
$\therefore$ Required number of ways $= 10 - 1 = 9$
[Since only one way in which the same ball have a same box]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.