The answer to the b part is
I bet you wonder why. Look at the following webpage.
Derangement -- from Wolfram MathWorld
Please help in the following problem...
There are 8 envelops and 8 corresponding letters. Find the probability that :-
a) At least 2 letters go to the wrong envelops.
b) None of the letters go in to the right envelop.
Please help...any suggestion will be welcomed.
The answer to the b part is
I bet you wonder why. Look at the following webpage.
Derangement -- from Wolfram MathWorld
Hello, skyskiers!
There are: . possible outcomes.There are 8 envelopes and 8 corresponding letters.
Find the probability that:
a) At least 2 letters go to the wrong envelopes.
This is a bit of a "trick question".
Is there a way for exactly one letter to be in the wrong envelope?
Imagine . . . the other 7 letters are in the right envelopes.
. . Can the 8th one go into a wrong envelope? . . . No.
So it is impossible for exactly one letter to be misplaced.
That is, if any are misplaced, there will be at least two misplaced.
There is exactly one way for the letters be matched to their envelopes.
. .
The rest of the time, there will be at least 2 misplaced.
Therefore: .
This is a messy problem and has an obscure solution.b) None of the letters go in to the right envelope.
An arrangement of objects in which no object is in its proper position
. . is a derangement of the objects.
We want the number of derangements of 8 objects:
It can be found by: .
. . Imagine . . . an exponent becomes a factorial!
We have: .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
Therefore, the probability is: .