EXAMPLE 1.6.5

A couple is expecting the birth of a baby. If the child is a girl, they will choose her first name and middle name from this list of their favorite girls' names: Betty, Beverly, Bernice, Bonita, Barbie.

If the child is a boy, they will choose his first name and middle name from this list of their favorite boys' names: Biff, Buzz, Barney, Bart, Buddy, Bert.

In either case, the child's first name will be different from the middle name. How many two-part names are possible?

A. 50

B. 600

C. 61

D. 900

SOLUTION

In this case, the child's name will be either a girl's name or a boy's name, so the number of possible names will be the number of possible girl's names plus the number of possible boy's names.

Number of possible girl's names:

We form a two-part girl's name by making two dependent decisions.

1. Choose first name: 5 options.

2. Choose middle name: 4 options.

(5)(4) = 20 different two-part girl's names.

Number of possible boy's names:

We form a two-part boy's name by making two dependent decisions.

1. Choose first name: 6 options.

2. Choose middle name: 5 options.

(6)(5) = 30 different two-part boy's names.

Total number of two-part names

= number of girl's names + number of boy's names

= 20 + 30 =50