What represents the number of arrangements of 8 males and 8 females in line such that no two males are adjacent?

To understand why the correct answer is the representation of the number of arrangements of 8 males and 8 females in line such that no two males are adjacent, we need to analyze the problem step by step.

First, if we want no two males to be adjacent, we can start by arranging the 8 females. Placing these 8 females in a line allows us to visualize the possible positions where males can then be inserted. Arranging the females creates 9 potential gaps to place the males: one before the first female, one between each pair of females, and one after the last female.

To illustrate this, if we denote females as F, when lined up, the arrangement looks like this:

_ F _ F _ F _ F _ F _ F _ F _ F _

This demonstrates that there are indeed 9 gaps (represented by underscores) for the males to occupy.

Next, we need to place the 8 males in these 9 gaps. Choosing 8 out of these 9 gaps to place a male ensures that no two males ever occupy adjacent positions, as each selected gap has only one male. The selection of 8 gaps from 9 does not involve the use of combinations but rather fits straightforward