Counting

Apr 2010
11
0
In how many ways can 6 different candies be passed out to nine people if everyone can receive just one?

can we just assume that they have a choice of 6 each time? Like:
6*6*6*6*6*6*6*6*6

The next problem asks the same question but in this case everyone can have any number of candies....if the first part isn't right then this part won't be right.


Any clarification?
 
Apr 2010
41
15
India
In how many ways can 6 different candies be passed out to nine people if everyone can receive just one?

can we just assume that they have a choice of 6 each time? Like:
6*6*6*6*6*6*6*6*6

The next problem asks the same question but in this case everyone can have any number of candies....if the first part isn't right then this part won't be right.


Any clarification?
\(\displaystyle ^9c_6=\frac{9*8*7}{3*2*1}=84\)
 

Plato

MHF Helper
Aug 2006
22,461
8,633
In how many ways can 6 different candies be passed out to nine people if everyone can receive just one?
This is a simple permutation: \(\displaystyle ^9\mathcal{P}_6=\frac{9!}{(9-6)!}=9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4~\).
 

Soroban

MHF Hall of Honor
May 2006
12,028
6,341
Lexington, MA (USA)
Hello, chubbs145!

In how many ways can 6 different candies be passed out to nine people
if everyone can receive just one?

Plato is absolutely correct!



The next problem asks the same question
but in this case, everyone can have any number of candies.

For each of the 6 candies, there are 9 choices of people to give it to.

Answer: .\(\displaystyle 9^6 \:=\:531,\!441\) ways.