A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{4!}{6!} \)
\( \frac{4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5} \)
\( \frac{1}{30} \)

First, solve for \( \left|a + 2\right| \):

\( \left|a + 2\right| \) + 6 = 3
\( \left|a + 2\right| \) = 3 - 6
\( \left|a + 2\right| \) = -3

The value inside the absolute value brackets can be either positive or negative so (a + 2) must equal - 3 or --3 for \( \left|a + 2\right| \) to equal -3:

So, a = 1 or a = -5.

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.5km + 20.3km + 12.8km
total distance = 33.6km

By buying two shirts, Ezra will save $17 x \( \frac{10}{100} \) = \( \frac{$17 x 10}{100} \) = \( \frac{$170}{100} \) = $1.70 on the second shirt.

So, his total cost will be
$17.00 + ($17.00 - $1.70)
$17.00 + $15.30
$32.30

There are 4 3-passenger taxis available so that's 4 x 3 = 12 total seats. There are 15 people needing transportation leaving 15 - 12 = 3 who will have to find other transportation.