Suppose on this road trip there was limited room (hence the heinous crime of mixing skittles and m&ms). Rachael was limited to only brining 2 pairs of shoes out of the 8 pairs she has. How many different combinations of shoes could she bring?

To find the number of different combinations of shoes Rachel can bring, we can use the combination formula.

The number of combinations of selecting 2 pairs of shoes out of 8 pairs is given by the formula:

C(n, r) = \frac{{n!}}{{r!(n-r)!}}

where n is the total number of pairs of shoes and r is the number of pairs she wants to bring.

In this case, n = 8 and r = 2. Plugging in these values into the formula, we get:

C(8, 2) = \frac{{8!}}{{2!(8-2)!}}

Simplifying the expression:

C(8, 2) = \frac{{8!}}{{2!6!}}

C(8, 2) = \frac{{8 \times 7 \times 6!}}{{2! \times 6!}}

Canceling out the common terms:

C(8, 2) = \frac{{8 \times 7}}{{2 \times 1}}

C(8, 2) = \frac{{56}}{{2}}

C(8, 2) = 28

Therefore, Rachel can bring 28 different combinations of shoes on her road trip.