P & C math problem.

[manan.super007]

Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,4.What is the probablity that none of the objects occupy the place corresponding to its number
a- 17/24
b-3/8
c-1/2
d-5/8

[esledge]

The easiest and best way to solve is to actually list the cases in which none of the objects is in its "correct" place. It can't be that bad--there are only 4! = 24 total ways to arrange the objects, even when ignoring location constraints.

2143
2341
2413
------
3142
3412
3421
------
4123
4312
4321

I generated this list by putting a "wrong" object in first place, another "wrong" object in second place, then thinking "what two are left, and how can/must I place them?" [It also helps to list numbers in systematically increasing fashion, to make sure you don't miss anything.]

Take 2143, for example, and notice that I had no choice about the placement of 4 and 3 (if reversed, they would have been in the correct location). This is why a more math-based approach could backfire--it is too easy to lose sight of these unanticipated limitations.

The answer is 9/24 = 3/8.

[manan.super007]

Thanks forthe lucid explanation :)

[tommywallach]

Glad the team could help!

-t