Explanation on why 0!=1
Yesterday, I posted a tutorial on permutation but I said that I will explain why 0!=1 in my next topic , in case you missed the tutorial click here Permutation tutorial
Now let's start.
From my previous post, I stated that factorial notation formula is;
n! = n * (n - 1) * (n - 2) *..... 3 * 2 * 1
Which will only works when n is greater than 0.
Using the above formula,
6! = 6(6-1)(6-2)(6-3)(6-4)(6-5)
By simplyfying
6!= 6 * 5 *4 *3 * 2 * 1 ---------------eq(1)
Then
6!= 720 ---------------------------------eq(2)
Let's simplify 5!
5!= 5 * 4 * 3 * 2 * 1 ------------------ eq(3)
5!=120
By substituting 5!= 5 * 4 * 3 *2 *1 in eq(1)
Then we will have,
6! = 6 * 5!
By dividing both side by 6 then,
5! = 6!/6
From eq(2) 6!= 720
Substituting that, we the have
5! = 720/ 6
5!= 120
You can see that we get same answer
Do you get it?
Now we can say that,
4! =5!/5
4!= 120/5
4!= 24
Do you agree with that? If you are still confuse, Let's use the above formula to solve it.
4!= 4(4-1)(4-2)(4-3)
4!= 4 * 3 * 2 * 1
4!= 24
Hope you aren't confused anymore?
Now, let's proceed
3!= 4!/4
3!= 24/4
3!= 6
2!= 3!/3
2!= 6/3
2!= 2
1!= 2!/2
1!= 2/2
1!= 1
Then,
0!= 1!/1
0!=1/1
0!=1
There are some others ways to explain it but it will be more complicated for beginners because it require using advance mathematics topics.
Follow @hayzeed and visit our blog daily for more tutorial.
What is this witchcraft?
Kidding aside that's a cool math result, never would have guessed that zero factorial is equal to 1.
Lol. Thanks. Math is fun, Always visit my blog for more tutorial.
Tutorial on COMBINATION has been posted.
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