Колодий Н.А., Мазепа Е.А. Сборник задач и упражнений по теории вероятностей
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k
m
1
m
2
k
m
k
k
m
1
· m
2
· . . . · m
k
n
n k
k
{1, 2, . . . , k}
k
n (k 6 n)
n k
A
k
n
n k
n
n B
B
P
n
n
k
n (k 6 n)
n k
C
k
n
n k
A
k
n
= n · (n − 1) · . . . · (n − k + 1) =
n!
(n−k)!
P
n
= n!
C
k
n
=
n!
(n−k)!k!
=
n(n−1)...(n−k+1)
k!
.
9 · 10
5
= 900000
5
n
q = p
α
1
1
p
α
2
2
. . . p
α
n
n
p
i
α
i
0, 1, 2, . . . , 9
n
2 n
C
2
n
n
n × n
n
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(n −1)
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8
{1, 2, . . . , n}
{1, 2, ..., n}
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{a
1
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(n −2)!
{1, 2, . . . , 2n}
n
2
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n
n n
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n
k
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1
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n
} n
A
a
i
A
Ω n
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n
P
5
= 5! = 120
3!
P
6
3!
= 120
C
2
5
C
2
3
C
1
1
= 30
n k
1
a
1
k
2
a
2
k
m
a
m
(k
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n+m+s
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n
m
m
n
m
n
n m
C
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= C
n
n+m−1
n m
(b
1
, . . . , b
n+m−1
)
n m−1
(b
1
, . . . , b
n+m−1
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(m−1)
m
n m m−1
n+m−1 m−1
C
m−1
n+m−1
n m
n n + m − 1 n
C
n
n+m−1
10
5
7 3
1, 2, 3
5
n
1
n
2
n
3
m
n
k k 6 9
H
H
F A
H
H
H Ω
ω
Ω
Ω
A
A
ω ∈ A
A
A
n H
ν
n
(A) ,
k
n
(A)
n
k
n
(A) A
0 6 ν
n
(A) 6 1 ν
n
(∅) = 0 ν
n
(Ω) = 1
A ∩ B = ∅ ν
n
(A ∪ B) = ν
n
(A) + ν
n
(B)
n
H ν
n
(A)
P (A)