Exercices de dénombrement pour classes préparatoires

#
ˇ“(
ˇ“(
256 0 255
30 000
˘“
˘“

#
n
k a1, a2, . . . , ak
•
•
ai
ai=i i
ai
ˇ“
30
20 10
ˇ“
E p F n
E n P
X∈P(E)
X
ˇ“(
S[[1,30]] S
5S
ˇ“(
ˇ“(
n
ˇ“(
[[1,100]]
ˇ“(

#
ˇ“(
100 65 77 74
47 51 57
˘“
8
16
ˇ“
E=n S =P
A∈P(E)
A
ˇ“
n[[1, n]]
ˇ“
100
ˇ“

#
ˇ“
E n (X, Y )∈P(E)2X∩Y
ˇ“1
2
764 322 555
823
ˇ“
[[1,50]] [[1,11]]
ˇ“
E n S =P
(X,Y )∈(P(E))2
(X∩Y)
Z∈P(E)k(X, Y )
X∩Y=Z
S
X Y E {X×Y, X ×Y , X ×Y, X ×Y}
E2
Sϕ: (P(E))2−→ (P(E))2
(X, Y )7−→ (X, Y )
ˇ“
ˇ“
(x, y, z)∈(N\{0})3x+y+z= 60
ˇ“
10
20 150
ˇ“
{a, b, c, d}
d
ˇ“
1 8
32 23

#
x1, . . . , xnn x1+· · · +xn
tn
t1= 1
t2, t3, t4
tnt1, . . . , tn−1
ˇ“(
n
p
n
6×6 36
9
262 144
2n n n
n . . .
p{1, . . . , n}
{x1, . . . , xp}x1< x2<· · · < xp
{x1−1, . . . , xp−p}
tn{1, . . . , n}
tn+2 =tn+1 +tnt2n+1 =t2
n+t2
n−1t2n=t2
n−t2
n−2
t50