Uniform Possibilities: how many different outfits from 4 shirt colors, 3 pants colors
- Thread starter Djm
- Start date
My best advice to you is to brush up on your problem solving and pattern recognition skills. These two things truly are the basis of almost all of mathematics. It comes in very very handy, not just in assigned math problems in school, but also on-the-job applications and even real life tidbits like this. A good way to approach combination problems is to start with the simplest possible case and work your way up, examining any patterns you find along the way.
Start with the trivial case and assume the only options were black shirt and black pants. Well, obviously, you'd have 1 uniform. Now add in the possibility of navy blue pants, and you've got two possible uniforms. Add in the last possible pants color, khaki, and you've got three. Thus, you can see that if you limit yourself to a black shirt, you have three possibilities. But now what if you have two shirt colors to choose from? Well, you already know that there's three pants options for if you wear a black shirt. So how many pants options are there if you wear a white shirt? Why? Then how many uniforms total are there? Are you seeing a pattern now? If not, maybe consider what happens if you choose to wear a navy blue shirt. How many pants options are there for a navy blue shirt? Why? How many total uniforms? Why?
Start with the trivial case and assume the only options were black shirt and black pants. Well, obviously, you'd have 1 uniform. Now add in the possibility of navy blue pants, and you've got two possible uniforms. Add in the last possible pants color, khaki, and you've got three. Thus, you can see that if you limit yourself to a black shirt, you have three possibilities. But now what if you have two shirt colors to choose from? Well, you already know that there's three pants options for if you wear a black shirt. So how many pants options are there if you wear a white shirt? Why? Then how many uniforms total are there? Are you seeing a pattern now? If not, maybe consider what happens if you choose to wear a navy blue shirt. How many pants options are there for a navy blue shirt? Why? How many total uniforms? Why?
Looks simple to me (so I must be missing something...):
5 shirts with each pants...so 15
You're not "missing something," you're adding something in there that doesn't belong. There are four shirt colors, not five shirt colors.