How many ways are there to put 4 balls in 3 boxes if the balls are distinguishable...

[areallykoolkat]

How many ways are there to put 4 balls in 3 boxes if the balls are distinguishable but the boxes are not?

i really need help please!!!!!!!!!!!!

 

[Deleted member 4993]

How many ways are there to put 4 balls in 3 boxes if the balls are distinguishable but the boxes are not?

i really need help please!!!!!!!!!!!!

Suppose you had a red ball (R), blue ball (B), green ball(G) and a yellow ball (Y).

How many ways can you pick three balls out of those 4?

 

[pka]

How many ways are there to put 4 balls in 3 boxes if the balls are distinguishable but the boxes are not?

The answer can be found here.
The general solution is very complicated.

 

[Deleted member 4993]

How many ways are there to put 4 balls in 3 boxes if the balls are distinguishable but the boxes are not?

i really need help please!!!!!!!!!!!!

If you are not ready for Sterling numbers - as pka suggested - you can think this through for small numbers.

To put balls in the boxes - what are the restrictions?

Does every box must have a ball?

Does every ball need to get into a box?

Show some work.....

 

[ecoo]

The first step that I would take is to lay out the number of ways to put the balls into the boxes, regardless of uniqueness of the balls.

One way is to have 2 in a box, 1 in a box, and 1 in the last box. Are there any other ways?

After we know the ways to arrange the balls, it is time to factor in uniqueness. One arrangement for the balls is 2 in a box, 1 in a box, and 1 in a box. So how many ways can you arrange unique balls in this type of array? Using Khan's method of labeling the color of balls, one way would be to put blue and green in a box, red in a box, and yellow in the last box. How many arrangements for this scenario are there?