Question

1) 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 two-part names; Jacob Jacob is not a valid
possibility.)
a) 36
b) 12
c) 30
d) 11

Answer 1

C. 30

Explanation:

We have a list of names that need to be sorted in a specific order. For this, we will use a permutation. This can be found on a scientific calculator, however, I'll be using the equation.

`_nP_r=(n!)/((n-r)!)`

n = total number of objects

r = number of objects selected

In this instance, n will equal 6 since we have 6 different names to choose from and r will equal 2 since we are picking two names. Enter the values into the equation and evaluate.

`_6P_2=(6!)/((6-2)!)=30`

Therefore, there are 30 possible two-part names.