Number of Combinations

Combination is a selection of things or objects or any other from a collection. In combination order of objects is irrelevant.

Combination formula: C(n,r) = (n!) / (r!(n-r)!) ,

where, n gives number of things, and r gives number of times. In this article we will study about how to calculate the combinations using combinations calculator.

Understanding Combinations Formula is always challenging for me but thanks to all math help websites to help me out.

Steps to find the number of combinations are:

Step 1: Enter the value of 'n'
Step 2: Enter the value of 'r'

Step 3: Click the button 'calculate', the result will be display in below text box.

Ex 1: A bag has 14 bulbs. How many ways 7 balls can be chosen from among 14 bulbs?

Sol: The problem involves 14 balls, chosen 7 at a time.

Combination formula: C(n,r) = (n!) / (r!(n-r)!) ,

Here n = 14, r = 7

C(14,7) = (14!) / (7!(14 - 7)!) = (14xx13xx12xx11xx10xx9xx8) / (7xx6xx5xx4xx3xx2xx1) = 3432

Therefore 3432 different ways 7 bulbs can choose from 14 bulbs.

Ex 2: In a jar there are 25 candies. In how many ways 7 candies can be chosen from a jar?

Sol:The problem involves 25 candies, chosen 7 candies at a time.

Combination formula: C(n,r) = (n!) / (r!(n-r)!) ,

Here n = 25, r = 7

C(25,7) = (25!) / (7!(25 - 7)!) = (25xx24xx23xx22xx21xx20xx19) / (7xx6xx5xx4xx3xx2xx1) = 480700

Therefore in 480700 different ways 7 candies can be chosen from a jar.

Ex 3: Calculate the number of combinations; n = 20, r = 8.

Sol:  Combination formula: C(n,r) = (n!) / (r!(n-r)!)

Here, n = 20, r = 8.

C(20,8) = (20!) / (8!(20 - 8)!) = (20xx19xx18xx17xx16xx15xx14) / (8xx7xx6xx5xx4xx3xx2xx1) = 125970

Therefore combination = 125970.

Ex 4: There are 15 marbles in a box. How many ways 6 marbles can be chosen from among 15 marbles?

Sol: The problem involves 15 marbles, chosen 6 at a time.

Combination formula: C(n,r) = (n!) / (r!(n-r)!) ,

Here n = 15, r = 6

C(15,6) = (15!) / (6!(15 - 6)!) = (15xx14xx13xx12xx11) / (5xx4xx3xx2xx1) = 5005

Therefore 5005 different ways 6 marbles can choose from 15 marbles.

I am planning to write more post on The Derivative and Inverse Functions Examples. Keep checking my blog.

Number of Combinations Calculator – Practice Problems

Pro 1: How many ways 5 balls can be chosen from among 17 balls in a jar?

Ans: 6188

Pro 2: In a jar there are 7 red balls and 9 orange balls. In how many ways can 4 balls be chosen from a jar?

Ans: 1820

Pro 3: Calculate the number of combinations; n = 19, r = 6.

Ans: 27132