You have 50 each of the following kinds of jellybeans: red, orange, green, yellow. The jellybeans of each color are identical. How many different handfuls of 12 jellybeans are possible?

There are 455 different  handfuls of 12 jellybeans possible

Step-by-step explanation:

From the given information;

we are told that there exist 50 kinds of jellybean for each of these colors (red, orange, green, yellow)

Also the jellybeans of each color are identical.  

i.e Let say y represent the color of the jellybean.

Then y₁ = y₂ = y₃ = y₄ corresponds to each of these colors (red, orange, green, yellow)

The objective is to determine how many different handfuls of 12 jellybeans are possible?

So;

y₁ + y₂ + y₃ + y₄ = 12

Therefore; the number of different  handfuls of 12 jellybean possible can be computed by using the formula:

where;

r =12 jellybeans

k = 4  types of colors

There are 455 different  handfuls of 12 jellybeans possible