Question

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?

• A. 17/24
• B. 3/8
• C. 1/2
• D. 5/8

Answer 1

The correct option is C 1/2

Let the four places be

1

2

3

4

Now object 1 cannot occupy the place 1 ........(A)

Suppose object 2 occupies the place '1'.

Then other placements can be done in 6 ways as follows:

(1) 2 1 3 4
(2) 2 1 4 3
(3) 2 3 1 4
(4) 2 3 4 1
(5) 2 4 1 3
(6) 2 4 3 1

Here out of the six ways, only three are permissible, because (1), (3) and (6) are not permissible because of the non-fulfillment of condition (A).

$Hence,requiredprobabilityis\frac{3}{6}=\frac{1}{2}$

Similarly, you can allow objects 3 and 4 to occupy place 1 and in each case you can find that the probability is 1/2.