: ,
.
.
: n . (n ≤ M).
w = (1, 2,, n), ai , i - .
, .
n = 2 (1,2) (2,1)
.
: nM = M!/(M n)! = N (Ω)
.
, .
n = 3; (1,2,3) (2,1,3)
: CnM = nM/n!
1.
1 100. 2 . , < 10?
.
1 9 ? ( ) 29 = 36.
2.
n , / r ? ( )
.
n = n 2 : 2!=2 (n - 2) : (n - 2)! , :
- 1, - r + 2, - 2, - r + 3 => (n - r -1) , - n - r - 1, n
: 2(n - 2)!(n - r -1) .
: c , .
.
n , .. , . m . w = (1, 2,, m), ai , i - . , .
n = 3; (1,2,3) (2,1,3) .
: Mn.
.
, n = 3; (1,2,3) (2,1,3) .
: CnM+n -1.
n . 0 n. , . , . . ?
i j - . = - 1 + 2 + + m = n. : * ; || .
| * * * | * | | | | * * * * |
M = 6 .
n = 8
(3,1,0,0,0,4)
( )
M + n + 1 2 = M + n -1
n :
nM + n 1
(: . = . , - . = n . . = nM + n 1 = N (Ω), .. = .)
: , , , , . .
|
|
N . , , .. 1 . . . . 1/ N. Ω = { w 1, wN }. .
m , . . = m / N. () = m / N.
1
. , 5 6.
= {5 6}
N = 6
() = 1/3 (2 6- ).
W (A) = m / n, m , , n .
.
.
n , - . k , k/n ( n ). k/n n ,- . , : % . - . , , .
.
: G . . . . g - - -. . G , - G (.1). - g G g . .. - . . g , . . G , =, .: =S(g)/S(G), S(g) S(G) . g G S(g) S(G) g G.
: / 12 . 20 . , . . . : , . . -, . . 1 . (.2). . . (, ) . 60. . , ½x y½ ≤20 (. .). G =60 2, g = 60 2 - 2*0,5*(40*40) = 602- 402, p = (602- 402) / 602= 5 / 9.
: . , , ? 1: . , , ┴ . . 2 - -: OD = OC = R / 2 () (.3). -, . ∩ - - CD, > - ∆. . - , . : = CD / AB =1/2.
2: (.4) , AB: =(. AB)/ (. -) =1/3. 3: , . . () - -, . / . , ┴ - - (.5). - ∆, . A R / 2: =(. R / 2) / (. R) =1/2. : - - - . . . 3- . .
|
|
(- - . p): - ║- , . . 2 a. - . - 2 l (l < a) (.6). - , - . . : x . , j / . , : 1) - 2 a ┴ . 2) φ [ φ 1, φ 1+Δ φ ], - - Δ φ . φ 1. 3) x φ . . - . -: . . - (S) - p - (.7). , . ∩ . ., . - . ≤ l sin φ (s). P(∩.) = ( s)/( S) = 2 l / a π. (. s = 0ò π l sin φ d φ; . S = a π)
( ) ω
Ω
:
1. .
2. .
3. .
: = - ; Ā .
: ( =Ø)
=1+2++n, k . .. ij=Ø (i≠j), 1, 2, n .
1, 2, n , 1+2++n=Ω
,
1. Ω, Ø
2. , (+ , , / )
1. Ω ,
1. Ω, Ø
2. , Ā
3. , (+ , )
2. σ-, n ,n=1,2, Σn , Πn
2. (Ω, ,), : Ω , σ- , З , :
1. ()≥0 ( )
2. (Ω)=1 ( )
3. = Ø => (+)=()+() ( )
4. 1 כ 2 כ, ∩n = Ø => (∩n)=0 ( )
.