"The Heavenrich family of five people randomly picks a name of a family member from a hat to decide for whom to buy a present. What is the probability that nobody picks their own name? If someoone picks their own name, all the names are returned and everyone picks again. What is the probability that it took exactly two tries for everyone to pick a name of another family member"
Probability that none draws his own name from a hat
- Thread starter Infiniti
- Start date
pka
Elite Member
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- Jan 29, 2005
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Think of the problem this way.
Name the folks: A,B,C,D,E. There are (5!)=120 ways to rearrange that string.
One of them is B,A,C,E,D. But that is no good because C has drawn his/her own name.
Here is a good string: C,E,B,A,D. That is called a derangement (none in a correct place) .
I will tell that there are only 44 derangements of a five-string.
Can you finish?
Name the folks: A,B,C,D,E. There are (5!)=120 ways to rearrange that string.
One of them is B,A,C,E,D. But that is no good because C has drawn his/her own name.
Here is a good string: C,E,B,A,D. That is called a derangement (none in a correct place) .
I will tell that there are only 44 derangements of a five-string.
Can you finish?