Four different objects 1, 2, 3, 4 are distributed at random in four places marked 1, 2, 3, 4.
Four different objects 1, 2, 3, 4 are distributed at random in four places marked 1, 2, 3, 4. What is the probability that none of the objects occupy the place corresponding to its number?
Answer/Solution
3/8
Steps/Work
There are 4! i.e. 24 ways in which four objects can be arranged in four places. There are a total of 9 instances where the objects are not occupying the place corresponding to the given number. They are as follows:
(2, 1, 4, 3) (2, 3, 4, 1) (2, 4, 1, 3) (3, 1, 4, 2) (3, 4, 1, 2) (3, 4, 2, 1) (4, 1, 2, 3) (4, 3, 1, 2) (4, 3, 2, 1)
Hence, the required probability = 9/24 = 3/8.
ANSWER:B
(2, 1, 4, 3) (2, 3, 4, 1) (2, 4, 1, 3) (3, 1, 4, 2) (3, 4, 1, 2) (3, 4, 2, 1) (4, 1, 2, 3) (4, 3, 1, 2) (4, 3, 2, 1)
Hence, the required probability = 9/24 = 3/8.
ANSWER:B