Difference between revisions of "User:Saul/algebra"
(→Combinations and Permutations) |
(Binomial Theorem) |
||
| Line 12: | Line 12: | ||
Also note that:<br> | Also note that:<br> | ||
'''n choose k''' is the same as '''n choose (n - k)''' | '''n choose k''' is the same as '''n choose (n - k)''' | ||
| + | |||
| + | == Binomial Theorem == | ||
| + | <big>'''(a + b)<sup>n</sup> = <sub>k=0</sub>Σ<sup>n</sup>((n choose k)a<sup>k</sup>b<sup>n-k</sup>)'''</big> | ||
| + | |||
| + | === Approximation Using Binomial === | ||
| + | Calculating a number to the power of another can be approximated by the following formulae:<br> | ||
| + | <big>'''(1 + x)<sup>n</sup> = 1 + nx + (n(n-1)x<sup>2</sup>)/2! + (n(n-1)(n-2)x<sup>3</sup>)/3! + (n(n-1)(n-2)(n-3)x<sup>4</sup>)/4! ...'''</big><br> | ||
| + | Note: This is unending so the more steps you take the more accurate the number will be, however usually 3-4 steps is enough. | ||
Revision as of 03:37, 25 September 2019
Contents
Combinations and Permutations
Permutations/Pick
A permutation is a sequence where the order does matter.
This is often notated by n pick r where n is the data set - say 40 lotto balls and r is the selection count - say 8 balls.
The general formulae for permutations is:
P = n! / (n-k)!
Combinations/Choose
A combination is a sequence where the order does NOT matter.
This is often notated by n choose r - n and r mean the same thing as in pick.
The general formulae for combinations is:
C = n! / ((n-k)!k!)
Also note that:
n choose k is the same as n choose (n - k)
Binomial Theorem
(a + b)n = k=0Σn((n choose k)akbn-k)
Approximation Using Binomial
Calculating a number to the power of another can be approximated by the following formulae:
(1 + x)n = 1 + nx + (n(n-1)x2)/2! + (n(n-1)(n-2)x3)/3! + (n(n-1)(n-2)(n-3)x4)/4! ...
Note: This is unending so the more steps you take the more accurate the number will be, however usually 3-4 steps is enough.
