Question

In mathematics, the factorial of a non-negative integer N, denoted by N!, is the product of all positive integers less than or equal to N. The factorial operation is encountered in many areas of mathematics, notably in combinatorics, algebra, and mathematical analysis. Its most basic occurrence is the fact that there are N! ways to arrange N distinct objects into a sequence (i.e., permutations of the set of objects). Today, Ross is working on a complicated combinatorial problem and he needs to find out factorials of some small integers. Help him!!

Answer 1

Answer:

Selected members of the factorial sequence (sequence A000142 in the OEIS); values specified in scientific notation are rounded to the displayed precision

n n!

0 1

1 1

2 2

3 6

4 24

5 120

6 720

7 5040

8 40320

9 362880

10 3628800

11 39916800

12 479001600

13 6227020800

14 87178291200

15 1307674368000

16 20922789888000

17 355687428096000

18 6402373705728000

19 121645100408832000

20 2432902008176640000

25 1.551121004×1025

50 3.041409320×1064

70 1.197857167×10100

100 9.332621544×10157

450 1.733368733×101000

1000 4.023872601×102567

3249 6.412337688×1010000

10000 2.846259681×1035659

25206 1.205703438×10100000

100000 2.824229408×10456573

205023 2.503898932×101000004

1000000 8.263931688×105565708

10100 1010101.9981097754820

In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n:

{\displaystyle n!=n\times (n-1)\times (n-2)\times (n-3)\times \cdots \times 3\times 2\times 1\,.}

For example,

{\displaystyle 5!=5\times 4\times 3\times 2\times 1=120\,.}

The value of 0! is 1, according to the convention for an empty product.[1]

The factorial operation is encountered in many areas of mathematics, notably in combinatorics, algebra, and mathematical analysis. Its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there are n!.

The factorial function can also be extended to non-integer arguments while retaining its most important properties by defining x! = Γ(x + 1), where Γ is the gamma function; this is undefined when x is a negative integer