EXAMPLE 1.4.14

A couple is expecting the birth of a baby boy. They will name the child by choosing a first name and middle name from this list of their favorite boys' names: Jacob, Jonah, Joshua, Jeremy, James, Joseph. The first name will be different from the middle name. How many different two-part names are possible? (Example: Joseph, Jeremy, Jeremy Joseph, and Joshua James are three different, valid names; Jacob Jacob is not a valid possibility.)

A. 36

B. 12

C. 30

D. 11

SOLUTION

Choosing a first name and a middle name for the child requires us to make two decisions. However, these two decisions are dependent, because the result of the first choice affects the options that are available for the second choice.

i. Choose first name: 6 options;

ii. Choose middle name: 5 options (whichever name was chosen for the first name cannot be repeated for the second name).

According to the Fundamental Counting Principle the number of two-part names is

(6)(5) = 30.