Four different objects A,B,C,D are distributed at random in four places marked A,B,C,D. What is the probability that none of the objects occupy the place corresponding to its alphabet?
Four different objects A,B,C,D are distributed at random in four places marked A,B,C,D. What is the probability that none of the objects occupy the place corresponding to its alphabet?
The correct option is E None of these
We need to find out the number of ways in which each object doesn't occupy a place corresponding to its alphabet.
Then, the 1st place can be occupied by the letters B, C, D.
Similarly, the 2nd place can be occupied by the letters A, C, D.
The 3rd place can be occupied by the letters A, B, D.
The 4th place can be occupied by the letters A, B, C.
If we consider the letter D in the 1st place, the possible combinations are (D,A,B,C), (D,C,A,B) and (D,C,B,A).
Similarly, if we consider other letters in the 1st place, each will have 3 possible combinations.
So, the total no. of possible combinations = 3x3 = 9
And, total combinations possible without any restrictions = 4!
∴ Required probability = 924 = 38
None of these
We need to find out the number of ways in which each object doesn't occupy a place corresponding to its alphabet.
Then, the 1st place can be occupied by the letters B, C, D.
Similarly, the 2nd place can be occupied by the letters A, C, D.
The 3rd place can be occupied by the letters A, B, D.
The 4th place can be occupied by the letters A, B, C.
If we consider the letter D in the 1st place, the possible combinations are (D,A,B,C), (D,C,A,B) and (D,C,B,A).
Similarly, if we consider other letters in the 1st place, each will have 3 possible combinations.
So, the total no. of possible combinations = 3x3 = 9
And, total combinations possible without any restrictions = 4!
∴ Required probability = 924 = 38
