Algebra
Wednesday, 25 May 2022
C1_Algeb-Proba Page 1
C1_Algeb-Proba Page 2
2, 4, 8, 16
C1_Algeb-Proba Page 3
a_9 = a_1r^(n-1)
a_9 = (27)(1/3)^(9-1)
a_9 = 1/243
0, 3, 6, 9, 12, 15, 18, 21, 24
C: Combination, Shift Divide (Depends on brand of Calcu)
r order, ex th term, r
, 0th term, r
0, and so on…
0
,
,
0
C1_Algeb-Proba Page 4
0
0
0
0
0
C1_Algeb-Proba Page 5
Principle of Counting
Wednesday, 25 May 2022
LETTER LETTER DIGIT DIGIT DIGIT
26 x 25 x 9 x 10 x 10 = 585,000
52
52
52
= 140608
b.
52, 51, 50 = 132,600
a.
___H___, ___T___, ___U___,
5, 6, 6 = 180
H = 2, 3, 4, 5, 8
T = All
U = All
d. Multiples of 5
___H___, ___T___, ___U___,
H = 2, 3, 4, 5, 8
T = All
U = 0,5
5, 6, 2 = 60
C1_Algeb-Proba Page 6
b.
___H___, ___T___, ___U___,
H = 2, 3, 4, 5, 8
T = All
U = 0,2,4,8 (Even)
5, 6, 4 = 120
c. Less than 440
___H___, ___T___, ___U___,
Case 1: 300 below
H = 2, 3
T = All
U = All
2, 6, 6 = 72
Case 2: 439 to 400
H=4
T = 0, 2, 3
U = All
1, 3 , 6 = 18
Total = 72 +18 = 90
0, 2, 3, 4, 5, 8
a. 3-digit numbers
___H___, ___T___, ___U___,
b. even numbers
___H___, ___T___, ___U___,
H = 2, 3, 4, 5, 8 (All except 0)
T = 5 numbers (All except H digit)
U = 4 numbers (All except H and T)
5, 5, 4 = 100
Case 1: Units = 0
H = 4 numbers (All except 0 & T dig)
T = 5 numbers (All except 0)
U = 1 number (0)
4,5,1 = 20
Case 2: Tens = 0
H = 4 numbers (All except 0 and U dig)
T = 1 number (0)
U = 3 numbers (2, 4, 8)
4, 1, 3 = 12
Case 3: No zero digit
H = 3 numbers (All except 0, T, and U dig)
T = 4 numbers (All except 0 and U dig)
U = 3 numbers (2, 4, 8)
3, 4, 3 = 36
Total = 20 + 12 + 36 = 68
! = Factorial
Calcu: x!
If all elements are being arranged = n!
a.
b. Circular permutation, (n-1)! (All elements are being arranged)
a. Without restrictions (All elements are arranged)
___, ___, ___, ___, ___
5, 4, 3, 2, 1 = 5! = 120
C1_Algeb-Proba Page 7
5, 4, 3, 2, 1 = 5! = 120
b.
`
G
G1, G2
2, 1
B
B1, B2, B3
3, 2, 1
c.
B1, B2, B3, G (G1, G2)
(4, 3, 2, 1) x (2, 1)
= 48
n! = arrange all elements
n1!n2!...nr! = eliminate arrangement of identical elements
7.
8.
3! = 3 letter D
4! = 4 identical red flags
3! = 3 identical white flags
1! = 1 blue flag
8C3 = 56
(7C3) x (5C2) = 350
C1_Algeb-Proba Page 8
3*2*1*2*1 + 2*1*3*2*1 = 24
(7C3) x (5C2) = 350
a.
12C4 = 495
b. A, B, 10 others
A and B will not attend together
Case 1: A will attend
1 x 10C3 = 120
Case 2: B will attend
1 x 10C3 = 120
Case 3: A and B will not attend
10C4 = 210
Total = 120+120+210=450
C1_Algeb-Proba Page 9
c. A, B, 10 others
A and B will attend together
Case 1: A and B will attend
1 x 1 x 10C2 = 45
Case 2: A and B will not attend
10C4 = 210
Total = 45+210=255