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# What is 11 factorial ?

Steps to calculate factorial of 11

To find 11 factorial, or 11!, simply use the formula that multiplies the number 11 by all positive whole numbers less than it.

Let’s look at how to calculate the Factorial of 11:

11! is exactly :
39916800
Factorial of 11 can be calculated as:
11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

## What is Factorial?

A factorial, denoted by an exclamation mark (!), is a mathematical operation applied to natural numbers. It represents the product of all the integers from 1 up to the number itself. The factorial of 11, which is symbolized as 11!, therefore involves multiplying all numbers from 1 to 11. Understanding 11! is significant because it helps in the calculation of permutations, combinations, and various probability-related problems in mathematics.

## Formula to Calculate the Factorial of [Number]

The general formula for calculating the factorial of a number n is n! = n × (n-1) × … × 3 × 2 × 1. Applying this formula to the number 11, the factorial of 11, or 11!, is calculated as:

11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

By successively multiplying these numbers, you arrive at the value of 11 factorial, which is a large integer used in various mathematical applications.

## What is the Factorial of [Number] Used For?

The factorial function, particularly the factorial of 11, has intriguing applications across different fields of mathematics. In combinatorics, 11! represents the number of ways to arrange 11 distinct objects. It’s crucial in probability theory for calculating the odds of specific sequences or combinations occurring. Furthermore, factorials are invaluable in computing binomial coefficients which are part of binomial theorem expansions.

## Exercises

• Calculate the number of distinct arrangements for a soccer team photo with 11 players.
• If you have a box with 11 colored balls, how many ways can you line them up on a shelf?

## Solutions to Exercises

For both of the given exercises, the solution lies in understanding the concept of factorials as representations of permutations. Since there are 11 players or colored balls, the number of distinct arrangements or permutations for both scenarios would simply be 11!.

## Frequently Asked Questions

### Q: What is the numerical value of 11 factorial (11!)?

A: The numerical value of 11 factorial (11!) is 39,916,800.

### Q: Why is the factorial of 0 equal to 1?

A: The factorial of 0 is defined to be 1 because there is exactly one way (no way) to arrange zero objects, providing a base case for the recursive definition of factorial.

### Q: Can factorial be applied to non-integer numbers?

A: Factorial is generally defined only for non-negative integers. However, the gamma function extends the concept to non-integer values, except for negative integers and zero.