why factorial of 1 and 0 is equale i.e. 1?

Question

in mathematics factorial of 1(1!) and 0 factorial(0!) is equal to 1? but both are different digits cannot be equal.so y the factorials are equal??
explain logically and keeping in mind mathematics....

Answer 1

linlyons is not only wrong....but overconfident in his incorrect assumption

Here's the correct explanation:

You already know that factorials are that number multiplied by all integers below it until 1.

Well for 1!, you can pretty much figure out that it's 1.

However, for 0!, you must use this method:

look at other factorials (4!, 3!, 2!, etc...)
since 4! = 4*3*2*1 and 3! = 3*2*1
that would mean that 4! = 4*3!
so 3! = 4!/4
the same applies to 2! = 3!/3
therefore, you can conclude that every factorial equals the next consecutive number's factorial divided by that number

So 1! = 2!/2 = (2*1)/2 = 1
So 0! = 1!/1 = 1/1 = 1

So both 1! and 0! equal 1.....
anything else you need to know besides that?

Answer 2

Factorial's give you a string of numbers to multiply and tell you what number to start with.

5! = 5 * 4 * 3 *2 * 1

Each time you multiply by 1 less til u get down to 1.

so 1! you start with 1 so you are already at 1.
1! = 1

As for 0! I was told to remeber 0! is 1 because its the only thing that makes the math equations true...

if you said 0! was 0 then in multiplication anything times 0 would be 0 and that would make two many multiplication problems 0..

Since anything times 1 is that anything letting 0! equal 1 will prevent a bunch of terms cancelling in probability questions.

So 1! = 1 because it follows the rule of factorials
0! = 1 because it will detriment probility questions if it does not equal 1

hope that helped.

Answer 3

0! = 1 is just a definition. It's only convenient to define it this way , so that you can state that the C(m,n) = m!/(m-n)!. If m = n, then what would you do? Divide by 0? The only way that it can be done is this one. I don´t really see other points to do things this way.

Ana

Answer 4

0! is 1 by definition.

Answer 5

n!=n(n-1)!
1!=1 (from defination)
n=1
1!=1*0!
hence
0!=1
actually 0 factorial is defined as1