A combination is a method in Mathematics which involves selecting a certain number of items from the group of items. In combinations, the order of arrangements of the items is not considered important and therefore, the formula for Combinations is only based on selecting items with or without repetition. Combination calculator is the quick online tool which can evaluate the number of combinations possible for a given group of items.
Example 1: From a bag of 10 books if 4 books are taken out, then what is the number of ways of selecting these 4 booksconsidering no order without repetition?
nCr = n! / [r! (n – r)!]
Here, n= total number of items= 10
r= number of items selected= 4
So, 10C4 = 10! / [(4! *(10 – 4)!]= 10! /(4! * 6!)
This implies: 10C4= (10* 9* 8* 7) / (4* 3* 2* 1)=210.
Example 2: In abox there are pens of colors red, green, blue, pink, and black. How many different ways are possible to choose 4 pens considering no order?
In the above question, order of selection doesn’t matter but there is possibility of selecting pens with repetition!
So we use the formula: n+r-1Cr = (n+r-1)! / [r! * (n– 1)! ]
n= number of pen colors we can choose from= 5
r= number of pens actually picked= 4
So, n+r-1Cr = (5+4-1)!/ (4! *4!) = 8!/ (4! * 4!) = 70