5 coins how many combinations

How many outcomes are possible? How many outcomes are possible if 3 coins are tossed? How many possible outcomes are there if Four coins are flipped? How many possible outcomes are there when flipping a coin 11 times? Two coins are tossed and a six sided die is rolled how many outcomes?

If you flip a coin 2 times how many possible outcomes are there? How many outcomes if you flip 3 coins? If there are three coins and each is flipped once how many possible outcomes are there? If SamJoe and Debbie each flip a coin how many possible outcomes are there? If you toss a penny a nickel and a quarter how many possible outcomes? How many possible outcomes if each coin is flipped once? How many possible outcomes would be if three coins were tossed once?

How many possible outcomes would there be if three coins were each tossed onces? If you flip a coin 4 times how many possible outcomes are there? How many outcomes are possible if you toss n coins?

How many outcomes are possible if 4 coins are tossed together? What is the possible outcome of tossing 10 coins? If 3 two sided coins are tossed how many outcomes? How many possible outcomes would there be if thirty two coins were tossed once? You are counting all 5 orderings of 1 heads and 4 tails.

Zev Chonoles Zev Chonoles k 18 18 gold badges silver badges bronze badges. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Featured on Meta. Now live: A fully responsive profile. Understand the concept and try to solve the problem yourself. If there is problem related to concept, contact at sudhanshu.

In making a sum of money, he has 2 choices for each coin: include it, or not. One of those possibilities is 0 if he chooses not to include every coin in his selection.

Check out our factorial calculator for more information on this topic. The expression on the right-hand side is also known as the binomial coefficient.

We also use it in our other statistical calculator, called the binomial distribution calculator. If you visit this site, you'll find some similarities in the computations - for example, that binomial calculator uses our nCr calculator. Let's apply this equation to our problem with colorful balls.

We need to determine how many different combinations are there:. You can check the result with our nCr calculator. It will list all possible combinations , too! However, be aware that different combinations are already quite a lot to show. To avoid a situation where there are too many generated combinations, we limited this combination generator to a specific, maximum number of combinations by default.

You can change it in the advanced mode whenever you want. You may notice that, according to the combinations formula, the number of combinations for choosing only one element is simply n. On the other hand, if you have to select all the elements, there is only one way to do it.

Let's check this combination property with our example. Every letter displayed in the nCr calculator represents a distinct color of a ball, e. Try it by yourself with the n choose r calculator! By this point, you probably know everything you should know about combinations and the combination formula. If you still don't have enough, in the next sections, we write more about the differences between permutation and combination that are often erroneously considered the same thing , combination probability, and linear combination.

Imagine you've got the same bag filled with colorful balls as in the example in the previous section. Again, you pick five balls at random, but this time, the order is important - it does matter whether you pick the red ball as first or third.

Let's take a more straightforward example where you choose three balls called R red , B blue , G green. This is the crucial difference. By definition, a permutation is the act of rearrangement of all the members of a set into some sequence or order. However, in literature, we often generalize this concept, and we resign from the requirement of using all the elements in a given set. That's what makes permutation and combination so similar.

This meaning of permutation determines the number of ways in which you can choose and arrange r elements out of a set containing n distinct objects.

This is called r-permutations of n sometimes called variations. The permutation formula is as below:. Doesn't this equation look familiar to the combination formula? In fact, if you know the number of combinations, you can easily calculate the number of permutations:.

If you switch on the advanced mode of this combination calculator, you will be able to find the number of permutations. You may wonder when you should use permutation instead of a combination.

Well, it depends on whether you need to take order into account or not. For example, let's say that you have a deck of nine cards with digits from 1 to 9. You draw three random cards and line them up on the table, creating a three-digit number, e.

How many distinct numbers can you create? The number of combinations is always smaller than the number of permutations. This time, it is six times smaller if you multiply 84 by 3! It arises from the fact that every three cards you choose can be rearranged in six different ways, just like in the previous example with three color balls. Both combination and permutation are essential in many fields of learning.

You can find them in physics , statistics, finances, and of course, math. We also have other handy tools that could be used in these areas.