This section covers permutations and combinations.
The number of ways of arranging n unlike objects in a line is n! (pronounced ‘n factorial’). n! = n × (n – 1) × (n – 2) ×…× 3 × 2 × 1
How many different ways can the letters P, Q, R, S be arranged?
The answer is 4! = 24.
This is because there are four spaces to be filled: _, _, _, _
The first space can be filled by any one of the four letters. The second space can be filled by any of the remaining 3 letters. The third space can be filled by any of the 2 remaining letters and the final space must be filled by the one remaining letter. The total number of possible arrangements is therefore 4 × 3 × 2 × 1 = 4!
In how many ways can the letters in the word: STATISTICS be arranged?
There are 3 S’s, 2 I’s and 3 T’s in this word, therefore, the number of ways of arranging the letters are:
Rings and Roundabouts
When clockwise and anti-clockwise arrangements are the same, the number of ways is ½ (n – 1)!
Ten people go to a party. How many different ways can they be seated?
Anti-clockwise and clockwise arrangements are the same. Therefore, the total number of ways is ½ (10-1)! = 181 440
The number of ways of selecting r objects from n unlike objects is:
There are 10 balls in a bag numbered from 1 to 10. Three balls are selected at random. How many different ways are there of selecting the three balls?
10C3 =10!=10 × 9 × 8= 120
A permutation is an ordered arrangement.
nPr = n! .
In the Match of the Day’s goal of the month competition, you had to pick the top 3 goals out of 10. Since the order is important, it is the permutation formula which we use.
There are therefore 720 different ways of picking the top three goals.
The above facts can be used to help solve problems in probability.
In the National Lottery, 6 numbers are chosen from 49. You win if the 6 balls you pick match the six balls selected by the machine. What is the probability of winning the National Lottery?
The number of ways of choosing 6 numbers from 49 is 49C6 = 13 983 816 .
Therefore the probability of winning the lottery is 1/13983816 = 0.000 000 071 5 (3sf), which is about a 1 in 14 million chance.
Looking for insights? It’s important to start off on the right foot. The way you get information and the survey questions you use play a big role in a successful survey.
Before you rush into writing your survey questions, ask yourself how you intend to use the answers from your survey. Are you going to ask direct questions? What about categorical questions? Once you know the goals of your survey and the information you’d like to collect, you’ll be able to choose survey question types easily.
Survey questions can use either a closed-ended or open-ended format to collect answers from individuals. And you can use them to gather feedback from a host of different audiences, including your customers, colleagues, prospects, friends, and family.
Before you decide on the different types of survey questions to use, let’s review each of your options. These include:
This list features the best types of survey questions, so once you master using them, you’ll be set to write surveys like a pro!
Below are some of the most commonly used survey question types and how they can be used to create a great survey. To see what each type of survey question might look like, visit the sample survey questions page.
Multiple choice questions are the most popular survey question type. They allow your respondents to select one or more options from a list of answers that you define. They’re intuitive, easy to use in different ways, help produce easy-to-analyze data, and provide mutually exclusive choices. Because the answer options are fixed, your respondents have an easier survey-taking experience.
Perhaps, most important, you’ll get structured survey responses that produce clean data for analysis.
Multiple choice questions come in many different formats.
The most basic variation is the single-answer multiple choice question. Single answer questions use a radio button (circle buttons representing options in a list) format to allow respondents to click only one answer. They work well for binary questions, questions with ratings, or nominal scales.
Here’s how a single-answer question can look:
Multiple-answer multiple choice questions are commonly shown with square checkboxes. They allow respondents to check off all the choices that apply to them. For example, "In which of the following ways do you use our product?"
A common drawback of multiple choice questions is that they force you to limit responses to a predetermined list of options. This can cause bias in your results. What if none of your answer options apply to your respondents? They might just choose a random answer, which could impact the accuracy of your results.
You can solve this problem by adding an “other” answer option or comment field. It should be listed at the end of all your choices. When respondents see it, they know they have the option of answering your question in their own words instead of yours.
In rating scale questions (sometimes referred to as ordinal questions), the question displays a scale of answer options from any range (0 to 100, 1 to 10, etc.). The respondent selects the number that most accurately represents their response.
With ranking questions and numerical rating scales it’s important to give the respondent context. For instance, imagine you asked the question, “how much do you like ice cream?” Without explaining the value of the numbers on your scale, a numerical rating scale might not make much sense.
Chances are you’ve seen this question type before. Likert scale questions are the “do you agree or disagree” questions you often see in surveys, and are used to gauge respondents’ opinions and feelings.
Likert scale questions give respondents a range of options—for example, starting at “not at all likely” scaling all the way up to “extremely likely”. That’s why they work well to understand specific feedback. For example, survey questions for employees often use a Likert scale to measure their opinions or attitudes on a range of topics.
If you want to ask a few questions in a row that have the same response options, matrix questions are your best option. A series of Likert scale questions or a series of rating scale questions can work well as a matrix question. Matrix questions can simplify a lot of content, but it’s important to use them carefully. Very large matrices, like the one below, can be confusing and difficult to take on mobile devices.
The dropdown question is an easy way to display a long list of multiple choice answers without overwhelming your respondents. With it, you can give them a scrollable list of answers to choose from.
Sometimes, showing all answer options at once can offer your respondents useful context about the question. Keep that in mind whenever you consider using more than one dropdown question in your survey.
When it comes to analyzing data, open-ended questions aren’t the best option. It’s not easy to quantify written answers which is why text boxes are better for providing qualitative data. Allowing your respondents to offer feedback in their own words could help you uncover opportunities that you may have otherwise overlooked. However, if you’re looking for data to analyze, you may want to engage in some quantitative marketing research and utilize closed questions.
Pro tip: Pair closed-ended questions with open-ended ones to better understand and address your quantitative data. For example, after the Net Promoter question, you can ask:
Use demographic survey questions if you’re interested in gathering information about a respondent’s background or income level. When properly used, these types of questions in a questionnaire allow you to gain better insights on your target audience. Demographic questions are powerful tools to segment your audience based on who they are and what they do, allowing you to take an even deeper dive in on your data.
Classic demographic questions ask for information like age, gender, and occupation. They can even ask for the respondent’s relationship status:
Once you get the hang of survey question types, you’ll quickly get the most out of your data. Learning which survey question type to use helps you focus on the most important information you need from respondents. Until then, you can use our survey creation tools to help you choose the best questions for your survey.
A ranking question asks respondents to order answer choices by way of preference. This allows you to not only understand how respondents feel about each answer option, but it also helps you understand each one’s relative popularity.
It’s important to keep in mind that ranking questions can take more time to answer. So try not to use them if other question types can provide the data you need. Also, only use them when you’re confident that respondents are familiar with each answer option. Otherwise, they’ll be next to impossible to answer accurately and honestly.
For instance, in the question below, respondents need to be familiar with each show before they can compare them.
Our image choice question type allows you to use images as answer options. This works great when you want respondents to evaluate the visual qualities of something, such as an ad or a logo. It can also provide a breath of fresh air for respondents, as it gives them a break from reading.
Want to get real-time, gut reaction feedback on an image? Use a click map question! Add an image to your survey and ask survey takers to click a certain spot on the image. For example, you could ask what item on a shelf is most appealing, or which part of your website is most user friendly.
Need respondents to upload their resume? A headshot? Their ID? You can collect whatever you need as a PDF, PNG, or Doc file. And once your responses come back, you can easily download the files.
Give respondents a chance to evaluate something on a numerical scale with our slider question type. They’re interactive, which can make them fun to answer, and they allow you to quantify respondent sentiment at both an individual and aggregate level.
Benchmarkable questions aren’t necessarily presented in a specific format, but they’re special in that they allow you to compare yourself to other survey creators who asked the same question.
Benchmarkable questions range widely, and they can be used for different audiences (employees, customers, etc.). To find one for your survey, you can either use our question bank or one of our survey templates. Any question that has a small bar chart icon at the top means it’s benchmarkable.
Now that you know the different survey questions you can ask, you’re ready to start creating your survey! Here’s some advice to keep in mind as you begin:
Creating a great survey doesn’t have to be difficult. Don’t let the design of a questionnaire throw you. You could create one in minutes by choosing from one of our hundreds of free, expert-designed survey templates built by our in-house subject-matter experts and survey scientists.
Prefer to create a survey from scratch? Use our Question Bank to start populating your survey with ready-made questions that can help you get the answers you need. Either way, you’re sure to have a survey our methodologists say will leave you with unbiased results.
Are your surveys ready to go mobile? Roughly 3 in 10 people taking SurveyMonkey surveys in the U.S. do so on a smartphone or tablet. Here’s a quick checklist on the different survey questions you should ask and how to format your survey to ensure it’s mobile-optimized and mobile-friendly.
We can all benefit from someone proof-reading our work. Surveys are no exception.
Share your survey with colleagues, friends, family, and anyone else who has a vested interest in its success before you send it. Who knows? They might be able to help you spot errors or areas for improvement!
It’s important to know which survey question type to use and when to use it. Once you’re familiar with different survey questions, you’ll be able to focus on what you need from respondents, getting you far better data than ever before.