Question

a couple has narrowed down the choices of a name for their new baby to first names and middle names. how many different​ first- and​ middle-name arrangements are​ possible?

Answer 1

There are 28 ways in which a couple can choose the name of the baby for its name.

What is defined as the combination?

• A combination is an algebraic technique for determining the number of possible arrangements in a set of items in which the order of the selection is irrelevant.
• You can choose the items in just about any order in combinations. Permutations and combinations are often confused.

If we need to choose objects from two groups of x and n objects so that one object from each group is chosen, we can do so by calculating the combinations possible by:  

= ˣC₁  ×  ⁿC₁

Let 'x' be the set of first name = 7

Let 'n' be the set of second name = 4

Putting the values in formula;

= ⁷C₁ × ⁴C₁

= 7 × 4

= 28

Thus, there are 28 ways in which a couple can choose the name of the baby for its name.

To know more about the combination, here

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The complete question is-

A couple has narrowed down the choices of a name for their new baby to 7 first names and 4 second names.

How many different first- and second-name arrangements are possible?