There are 23 animals in the barn. Some are chickens some are goats. There are 80 legs in all. How many of each animal is there?

There are 17 goats and 6 chickens

Explaining: (1)  C + G = 23

As for legs:

(2)  2C + 4G = 80 (each C has 2 legs and each G has 4 legs)

Solving equation (1):  C = 23 - G

Substituting in equation (2)

2(23 - G) + 4G = 80

2G = 34

G = 17

C = 6

because they could drop even lower..

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.