Question

In how many ways could four people be divided into two groups of one person and one group of two people?Four people could be divided into two groups of one person and one group of two people ___ ways.(Type a whole number.)

Answer 1

Suppose the people are named Adam, Bob, Charlie and David.

Let's say the group with one person is made out of only Adam. The permutations for the other 3 are

Bob and Charlie, Bob and David, and Charlie and David.

We have 4 permutations if Adam is the group of one. If we repeat the same process for the others, we have 4 permutations for each one of them, therefore, the total amount of distinct groups is given by

`4\cdot4=16`

We have 16 distinct groups.