WISKUNDE
NOG OEFENINGE

Waarskynlikheid : antwoorde.

MATHEMATICS
MORE EXERCISES

1.
SEBRA : 5 letters.
1.
SEBRA : 5 letters
Aantal maniere = 5! = 5 x 4 3 x 2 x 1 = 120
Number of arrangements = 5! = 5 x 4 3 x 2 x 1
= 120
= 120
2.
ALABAMA : 7 letters; 4 A's
2.
ALABAMA : 7 letters; 4 A's
7!
Rangskikkings / Arrangements = ───   = 210
4!
3.1
MILLENIUM : 9 letters; 2 I; 2 L; 2 M
3.2
Rangskikking / Arrangement : L _ _ _ _ _ _ _ L
9!
7 letters bly oor : 7! rangskikkings
Rangskikkings / Arrangements = ─────
2! 2! 2!
7 letters remain : 7! arrangements
= 45 360
7 letters : 2 M ; 2 I
7!
Rangskikkings / Arrangements = ─────
2! X 2!
= 1 260
3.3
Rangskikking / Arrangement : L _ _ _ _ _ _ _ M
7 letters : 2 I
7!
Rangskikkings / Arrangements = ───
2!
= 2 520
4.1
MATHEMATICS : 11 letters; 2 A; 2 M; 2 T
4.2
Rangskikking/Arrangement: M*********M
11!
9 letters bly oor / 9 letters remain
Rangskikkings / Arrangements = ─────
4.2
Rangskikking/Arrangement: M*********M
11!
9 letters bly oor / 9 letters remain
2! 2! 2!
= 4 989 600
9!
Rangskikkings / Arrangements = ────
2! 2!
= 90 720
4.3
Rangskikking/Arrangement: A*********T
4.4
Rangskikking/Arrangement: S*********E
9 letters bly oor / 9 letters remain : 2 M
9 letters bly oor / 9 letters remain 2A; 2 M; 2 T
9!
9!
Rangskikkings / Arrangements = ───
Rangskikkings / Arrangements = ──────
2!
2! 2! 2!
= 181 440
= 45 360
5.
EXCALIBUR 9 letters
Rangskikking/Arrangement: X _ _ _ _ _ _ _ C
7 letters bly oor / 7 letters remain
Rangskikkings / Arrangements = 7! = 5 040
6.1
BARBADOS : 8 letters; 2 A; 2 B
6.2
Rangskikking/Arrangement: B******R
8!
6 letters bly oor / 6 letters remain : 2 A
Rangskikkings / Arrangements = ────
2! 2!
= 10 080
6!
Rangskikkings / Arrangements = ──
2!
= 360
6.3
Rangskikking/Arrangement: S******D
6.4
Rangskikking/Arrangement: A******R
6 letters bly oor / 6 letters remain : 2 A 2 B
6 letters bly oor / 6 letters remain 2B
6!
6!
Rangskikkings / Arrangements = ────
Rangskikkings / Arrangements = ──
2! 2!
2!
= 180
= 360
Rangskikkings / Arrangements = n(S) = 10 080
en / and n(A**R) = 360
360
P(A**R)  = ──────  = 0,036
10 080
7.
Rangskikkings/Arrangements : gggggbbbb of / or bbbbggggg
Aantal rangskikkings/Number of arrangements = 5! x 4! + 4! x 5! = 5 760
8.1
Aantal rangskikkings/Number of arrangement = 7! = 5 040
8.2
Beskou die twee biografieê as 'n eenheid
8.2
Consider the two biografies as a unit which
wat op 2! maniere gerangskik kan word.
can be arranged in 2! ways. There remain
Daar is dan nog 6 voorwerpe oor wat op
6 objects which can be arranged in 6! ways.
6! maniere gerangskik kan word.
Total number of arrangements = 2! x 6! = 1 440
Totale rangskikkings = 2! x 6! = 1 440

8.3
Beskou die fiksie boeke as 'n eenheid
8.3
Consider the fiction books as a unit which
wat op 3! maniere gerangskik kan word.
can be arranged in 3! ways. Consider the
Beskou die biografieê as 'n eenheid wat op
biografies which can be arranged in 4! ways.
4! maniere gerangskik kan word.
These two units can now be arranged in
Hierdie twee eenhede kan nou op 2!
2! ways.
maniere gerangskik kan word.
Total number of arrangements = 2! x 3! x 4!
Totale rangskikkings = 2! x 3! x 4! = 288
= 288
9.1
Aantal kodes/Number of codes = 21 x 21 x 10 x 10 = 44 100
9.2
Aantal kodes/Number of codes = 21 x 20 x 10 x 10 = 42 000
10.1
Enige plek/Any seat = 5! = 120
10.2
Beskou die dogters as 'n eenheid wat op
10.2
Consider the girks as a unit which can
2! maniere gerangskik kan word.
be arranged in 2! ways.
Daar is nou 4 "mense" wat op 4! maniere
There are now 4 "people" that can be arranged
gerangskik kan word.
in 4! ways.
Totale rangskikkings = 2! x 4! = 48
Total arrangements = 2! x 4! = 48