Distributing n distinct objects to r different people - Why is my method wrong? I saw this problem:
How do I distribute 5 different candies to 3 different students?
I decided to try and make a modified Stars and Bars formula to handle the different candies.
My Method:
Suppose I had 5 different candies:
A B C D E
and 2 bars for 3 different students: ||
combined: A B C D E | |
To find all the different combinations of candies and students, I need to do
$${\frac{7!}{2!}}$$
However, my answer was wrong. I'm not sure what the correct answer is, because the quiz I took did not show it.
Why is my method wrong?
You just have to affect one student to each candy. For each candy, you have $3$ different possibilities, so this gives
$$3^5=243$$
possibilities.
You just have to affect one student to each candy. For each candy, you have $3$ different possibilities, so this gives
$$3^5=243$$
possibilities.