Combinations (Make sets combining one from each group)

Find how many combinations you can make:

  1. You are rolling a six-sided die one time and flipping a coin one time.  How many different combinations can you get? $6 \text{ die sides} \times 2 \text{ coin sides} = \mathbf{12 \text{ combinations}}$
  2. You are rolling a six-sided die two times and flipping a coin twice.  How many different combinations can you get? $6 \text{ die sides} \times 6 \text{ die sides} \times 2 \text{ coin sides} \times 2 \text{ coin sides}= \mathbf{144 \text{ combinations}}$
  3. You packed for a two day trip and brought two each of shorts, shirts, socks, underwear, and hats.  On the first day, how many different outfits might you put together from these items? $2 \text{ shorts options} \times 2 \text{ shirt options} \times 2 \text{ sock options} \times 2 \text{ underwear options} \times 2 \text{ hat options}= \mathbf{32 \text{ outfits}}$
  4. You are at an ice cream shop with 20 flavors of ice cream and two types of cone.  How many different cones might you put together?  $20 \text{ ice cream options} \times 2 \text{ cone options} = \mathbf{40 \text{ cones}}$
  5. If, at the same ice cream shop, you are choosing two flavors of ice cream and a type a cone, how many different cones might you put together? $20 \text{ ice cream options} \times 20 \text{ ice cream options} \times 2 \text{ cone options} = \mathbf{800 \text{ cones}}$
  6. If you are wrapping a gift and can choose amoung 5 types of wrapping paper and 3 types of ribbon, how many differently wrapped packages can you make? $5 \text{ paper options} \times 3 \text{ ribbon options}  = \mathbf{15 \text{ packages}}$
  7. If you are choosing a special card to go with that gift and can choose from among 6 cards, 3 different envelopes, and 2 types of confetti (or no confetti at all), how many different cards can you make? $6 \text{ card options} \times 3 \text{ envelope options}  \times 3 \text{ confetti options} = \mathbf{54 \text{ cards}}$
  8. You are putting together a summer schedule.  You are choosing between a math or a physics class, a horsebackriding or cooking camp, and either yoga, pilates, or karate competitions. If you choose one of each, how many different summer schedules can you make? $2 \text{ class options} \times 2 \text{ camp options}  \times 3 \text{ competition options} = \mathbf{12 \text{ summer schedules}}$