i just need help with factorials
I assume you know what a factorial is:
1! = 1
2! = 1x2 = 2
3! = 1x2x3 = 6
N! = 1x2x3x...x(N-1)xN
They occur often in probability theory.
Please ask a more specific question about factorials. I have no idea what else to tell you.
what is the explicit formula for the nth factorial? is there one without n*(n-1)*(n-2) and so forth?
No, drwls is correct; N! = 1*2*3...*N.
However, when using factorials, short-cuts and simplifications will often be present. For example, the formula for counting the number of ways one can deal two cards from a standard 52-card deck is:
52! / 2!(52-2)!
Well, calculating 52! by itself is an onerous task. However, we can simplify. 52!/50! cancels to 51*52, and 2! is simply 1*2=2. So, the answer is 51*52/2 = 1326.
I hope this helps
Why is 0! equal to one? write back asap!!
-concerned student seeking help
Good question! The value of 0! (0 factorial) being equal to 1 may seem counterintuitive at first, but there is a logical reason behind it.
To understand why 0! is equal to 1, let's look at the definition of factorials:
0! = 1
1! = 1
2! = 1 * 2 = 2
3! = 1 * 2 * 3 = 6
...
When we calculate factorials, we multiply all the positive integers from 1 up to the given number. For example, 3! is calculated as 1 * 2 * 3. However, if we apply the same logic to 0!, we would need to multiply all the positive integers from 1 up to 0, which is not possible because there are no positive integers between 1 and 0.
So, to maintain the pattern and consistency of factorials, mathematicians have defined 0! to be equal to 1. This convention allows factorials to be defined for every positive integer and extends the usefulness of the factorial concept.
I hope this explanation helps you understand why 0! is equal to 1. If you have any further questions, feel free to ask!