Combinatorics: Gift Giving at a Party

[Shoney45]

Homework Statement

Each of ten employees brings one distinct present to an office party. Each present is given to a randomly selected employee by Santa, and any employee can get more than one present. What is the probability that at least two employees receive no presents?

Homework Equations

P,(n,k) C(n,k)

The Attempt at a Solution

Since this is a probability problem, I first need to find the total number of ways to distribute the presents = my denominator = 10^10.

So I am imagining ten buckets into which I wish to place ten distinct presents. I want to place eight presents into eight buckets, and then find the total number of ways there are to place the remaining two presents into those eight buckets. The total number of ways for me to place the first eight buckets is 8^8 (since repetition is allowed) which then leaves me with P(8,2) ways to distribute the other presents such that two employees are left with zero presents.

Thus my answer is [8^8 x P(8,2)]\10^10

 

[lanedance]

not quite as it says "at least 2 employees receive no present" which, among others, includes the case when 1 person gets all the pressies