Combinations Replacement Calculator
Utilize the user-friendly tool Combinations Replacement Calculator and get the different combinations of a set instantly. Simply enter the input values of n, r in the respective input fields, and click the calculate button to get the result in a fraction of seconds along with detailed work.
Combinations Replacement Calculator: Have you ever wondered how many different combinations can be made out of a set of elements? Don't Fret as you can take the help of the online tool for Combinations over here. It might be tedious to list out every single possible combination and find the total. Thus, to overcome all such tedious calculations we have provided a quite user-friendly tool that displays the possible number of combinations in no time. Get the Combination Definition, Formula, Detailed steps to calculate Combinations with Replacement and Solved Examples in the coming modules.
Procedure to find Combinations with Replacement
Let us consider Combinations in which repetitions are allowed. That means each time you take an element from the set of n distinct objects you put it back to the set. You might feel the concept of Combinations with Replacement a bit complicated. Luckily, don't worry as we have listed the formula below.
CR(n, r) or C'(n,r) = (r+n-1)!/(r! * (n-1)!)
Where C'(n,r)) is the number of combinations with repetition or replacement
n is the total number of elements in the set,
and r is the number of elements you choose from this set.
Plugin the values of n, r in the corresponding formula, and simplify the equation further to get the number of Combinations with Replacement.
Example: Consider there are five flavors of ice cream butterscotch, vanilla, strawberry, chocolate, banana. You can have three scoops. How many variations are possible and we can repeat?
Solution:
From the given data n = 5
r =3
We know the formula for Combination with Replacement is C'(n,r) = (r+n-1)!/(r! * (n-1)!)
= (3+5-1)!/(3!*(5-1)!)
=(7)!/(3!*(4)!)
= 35
Therefore there are 35 ways of having three scoops from five different flavors.
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FAQs on Combinations Replacement Calculator
1. What is the formula for Combinations with Repetition?
The formula for Combinations with Repetition is (r+n-1)!/(r! * (n-1)!)
2. What is meant by Combination with Replacement or Repetition?
The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are allowed.
3. How to Calculate Combinations with Replacement?
Simply substitute the values of n, r in the formula for Combinations with Replacement and solve for equations respectively.
4. How to use Combinations Replacement Calculator?
Just input the corresponding data like n total number of items or objects, r sample elements value in the respective fields and click on the calculate button to get the different combinations with replacement.