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Learn about the benefits of the Ti-Nspire CX’s Computer Algebra System (CAS) over the Ti-Nspire CX without CAS. Examples in Algebra and Calculus are...
Factorial Calculator : n!
Below, compute Factorials using our handy Factorial Calculator.
You will also understand
-the n! Formula and its Real Life Usage
-its Recursive Property
-how to find Factorials using the TI-84 Calculator (Video)
Factorial Calculator
1) Enter an Integer
2) Press the ‘Compute Factorial’ button to compute the desired Factorial.
TI-84 Factorial Calculation
Using your TI84 Calculator, you can compute factorials this way:
To compute 5! (which is 5*4*3*2*1=120) press 5 , next press MATH and scroll right to PRB (Probability) , next select option 4:! as shown below:
Pressing ENTER gets you the correct solution:
Video: Compute Factorials using the TI-84 Calculator
Factorial n! - Formula, Real Life Usage and Properties.
Factorial Formula
n! = n*(n-1)*(n-2)*…*3*2*1
List of first 12 Factorials: [Christmas is coming 😉 ]
0!=1
1!=1
2!=2*1=2
3!=3*2*1=6
4!=4*3*2*1=24
5!=5*4*3*2*1=120
6!=6*5*4*3*2*1=720
7!=7*6*5*4*3*2*1=5,040
8!=8*7*6*5*4*3*2*1=40,320
9!=9*8*7*6*5*4*3*2*1=362,880
10!=10*9*8*7*6*5*4*3*2*1=3,628,800
11!=11*10*9*8*7*6*5*4*3*2*1=39,916,800
Real Life Usage: n! gives the number of rearrangements of n objects.
Example 1: 2 letters AB can be rearranged in 2!=2 ways:
AB and BA
Example 2: 3 letters ABC can be rearranged in 3!=6 ways:
ABC,ACB,BAC,BCA,CAB,CBA
Example 3: 4 letters ABCD can be rearranged in 4!=24 ways: Looking at ABC, the letter D can be placed before A, before B, before C or after C, that’s 4 ways. Multiply that by the 6 different arrangements yields 6*4 or 3!*4 = 24.
DABC,ADBC,ABDC,ABCD, DACB,ADCB, ….. , CBAD
Example 4: 4 letters ABCA can be rearranged in 4!/2!=12 ways:
AABC,ABAC,ABCA,BAAC,BACA,BCAA,CAAB,CABA,CBAA,DAAB,DABA,DBAA
Recursive Property: n! = n*(n-1)! or solved for n: n = n!/(n-1)!
Example 1: 3!=3*2! = 3*2
Example 2: 4!=4*3! = 4*6
Example 3: 5!=5*4! = 5*24
To compute n! just multiply the previously computed (n-1)! by n.
This may save a lot of time and mental energy.
Example 4: 10!/9! = 10*9*8*7*6*5*4*3*2*1 / 9*8*7*6*5*4*3*2*1 = 10 since all integers on top and bottom cancel out except for the 10 on top. No need to compute 10! or 9!.
Example 5: For the same reason 678!/677! = 678 .
Example 6: How about 102!/100! ? I will let you figure this one out…
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