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)
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Answer:
Correct Answer: 2. (9)
Solution:
- 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 $
