# How do you calculate how many possible combinations?

**Asked by: Amy Adams**| Last update: 18 June 2021

Score: 4.1/5 (3 votes)

**Combinations** are a way to **calculate** the total outcomes of an event where order of the outcomes does not matter. To **calculate combinations**, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time.

Additionally, How do you calculate the number of possible combinations?

The

**formula**for

**combinations**is generally n! / (r! (n -- r)!), where n is the total

**number**of possibilities to start and r is the

**number**of selections made.

Also question is, How many combinations of 4 items are there?. I.e.

**there**are

**4 objects**, so the total number of possible

**combinations**that they can be arranged in is

**4**! =

**4**x 3 x 2 x 1 = 24.

Similarly, How many combinations of 100 items are there?

It's fairly straightforward to calculate the number of

**combinations**of a given set of n elements, taken k at a time. Given

**100**, choose

**100**, there is only one

**combination**. Given

**100**, choose 99, there are

**100 combinations**. Given

**100**, choose 98, there are 161,700

**combinations**.

How many combinations of 20 items are there?

The number of

**combinations**that are possible with

**20**numbers is 1,048,575.

**17 related questions found**

### How many combinations of 7 items are there?

**7***6*5=210. So you get **7**∗6∗53∗2∗1 **7** ∗ 6 ∗ 5 3 ∗ 2 ∗ 1 = 35 ways.

### How many ways can 4 letters be arranged?

**How many** different **ways can** the **letters** P, Q, R, S be **arranged**? The answer is **4**! = 24. The first space **can** be filled by any one of the **four letters**.

### How many combinations of the numbers 1 2 3 4 are there?

Explanation: If we are looking at the **number** of **numbers** we can create using the **numbers 1**, **2**, **3**, and **4**, we can calculate that the following way: for each digit (thousands, hundreds, tens, ones), we have **4** choices of **numbers**. And so we can create **4**×**4**×**4**×**4**=**44**=256 **numbers**.

### How many combinations of 5 items are there?

In total you will find **5** × 24 = 120 possibilities.

### What is the formula for calculating permutations?

One could say that a **permutation** is an ordered combination. The number of **permutations** of n objects taken r at a time is determined by the following **formula**: P(n,r)=n! (n−r)!

### How many combinations of 12 numbers are there?

In your case, with **12 numbers**, the **number** is 12x11x10x... x2x1=479001600. This **number** is called "**twelve** factorial" and written **12**!, so, for example 4!= 4x3x2x1=24.

### How many combinations of 3 numbers are there?

There are, you see, **3** x 2 x 1 = 6 possible ways of arranging the **three digits**. Therefore in that set of 720 possibilities, each unique **combination** of **three digits** is represented 6 times. So we just divide by 6. 720 / 6 = 120.

### How many combinations are there of the numbers 1 2 and 3?

That is a total of 7 **combinations**.

### How many combinations of 6 numbers are there?

For any group of **6 numbers** and letters, there are a **possible** 720 **different** permutations or **combinations** that can be made.

### How many combinations of 10 numbers are there?

The **number** of **combinations** that are possible with **10 numbers** is 1,023.

### How many ways can 5 letters be arranged?

A **five**-**letter** word with no repeated **letters** has **5**! = 120 distinct arrangements.

### How many ways can 8 letters be arranged?

Note: **8** items have a total of 40,320 **different** combinations.

### How many ways can 10 letters be arranged?

**How many Ways** to **Arrange 10 Letters** Word STATISTICS? 50400 is the number of **ways** to **arrange 10 letters** (alphabets) word "STATISTICS" by using Permutations (nPr) formula.

### How many ways can you order 3 things?

= 5*4***3***2*1 = 120. Therefore, the number of **ways** in which the **3** letters can be arranged, taken all a time, is **3**! = **3***2*1 = 6 **ways**.