Ways to divide 8 different things into groups of 5 and 3

[lionely]

Homework Statement

In how many ways can 8 different things be divided into groups of 5 and 3.

Homework Equations

The Attempt at a Solution

I thought it be just be 8C5 X 8C3

but also might it be 8C5 x 3C3 since if you take 5 you only have 3 left to select from?

 

[Ray Vickson]

Homework Statement

In how many ways can 8 different things be divided into groups of 5 and 3.

Homework Equations

The Attempt at a Solution

I thought it be just be 8C5 X 8C3

but also might it be 8C5 x 3C3 since if you take 5 you only have 3 left to select from?

If you pick the three for one group you automatically leave 5 for the other group.

 

[HallsofIvy]

Another way to look at this is to arrange the 8 items in a row, then label those to go into the first group "0" and those to go into the second group "1". How many different way are there to order 5 "0"s and 3 "1"s?

 

[lionely]

Thank you