Permutations and Combinations 5 Question 2

2. 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 each in a box, could be placed such that a ball does not go to a box of its own colour is…. .

(1992, 2M)

Show Answer

Answer:

Correct Answer: 2. (9)

Solution:

  1. The number of ways in which the ball does not go its own colour box $=4 ! \quad 1-\frac{1}{1 !}+\frac{1}{2 !}-\frac{1}{3 !}+\frac{1}{4 !}$

$ =4 ! \frac{1}{2}-\frac{1}{6}+\frac{1}{24}=24 \quad \frac{12-4+1}{24}=9 $



NCERT Chapter Video Solution

Dual Pane