coolhabhi wrote:Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,4. What is probability that none of the objects occupy the place corresponding to it's number?
A) 17/24
B) 3/8
C) 1/2
D) 5/8
First of all, if we IGNORE the condition about where the objects can be placed, we can arrange the 4 different objects in
4! ways (=
24 ways).
So, we now must determine HOW MANY of those
24 arrangements are such that no objects occupy the location corresponding to its number.
A quick way to do this is to LIST acceptable outcomes.
IMPORTANT: We'll list each arrangement so that the first number represents the object that goes to location #1, the second number represents the object that goes to location #2, and so on.
So, for example, 3421 represents object #3 in location #1, object #4 in location #2, object #2 in location #3, and object #1 in location #4.
Let's be systematic:
Arrangements where object #2 is in location #1
The possible arrangements where NO object is in the correct location are as follows:
2143
2341
2413
Total # of arrangements =
3
Arrangements where object #3 is in location #1
The possible arrangements where NO object is in the correct location are as follows:
3142
3412
3421
Total # of arrangements =
3
Arrangements where object #4 is in location #1
The possible arrangements where NO object is in the correct location are as follows:
4123
4312
4321
Total # of arrangements =
3
Altogether, the number of arrangements where no object is in the correct location =
3 +
3 +
3 =
9
So, P(no object in correct location) =
9/
24 = [spoiler]3/8 = B[/spoiler]
Cheers,
Brent
