Reference
!
“!” is a symbol that represents a factorial.
For example, “3!” is equivalent to “3 × 2
× 1.”
(2)Combinations
A “combination” is the aggregate derived when an optional count is taken
from a particular collection of data, and the respective values are removed
from an equation.
If r is arbitrarily taken from the variant n, and the resulting combination of
numbers is expressed as nCr, the following expression is provided.
Cr
n
=
Pr
r!
n
n!
(n−r)! r!
=
Example
Take four variant numbers from the values “1”, “2”, “3”, “4”, “5”,
and “6.”
P
6×5×4×3
=
= 15
4!
4×3×2×1
6 4
(3)Probability
A “probability” expresses the likelihood that a certain phenomenon will
occur in comparison with all applicable phenomena.
If all phenomena are expressed numerically as n, and the likelihood of
phenomenon A occurring, as signified by r, in comparison to all phenomena is represented by P(A), the following expression is provided.
P (A) =
r
n
Example
When three out of ten lottery tickets contain a winning number,
determine the probability for drawing two consecutive winning
tickets.
Combination containing all phenomena:
Combination in which two out of ten tickets are drawn ··· 10C2 = 45
Combination in which two consecutive winning tickets are drawn:
Combination in which two out of three winning tickets are drawn ··· 3C2 = 3
The probability is calculated as follows.
3
1
=
45 15
163