Topic 12: Permutations, combinations and probability
For calculator:
Permutation: SHIFT + ×
n!: n + SHIFT + x⁻¹
Combination: SHIFT + ÷
Differences between permutations and combinations:
Both put ‘n’ objects into ‘r’ places, but combination doesn’t restrict positions (specific of r), while permutation does.
**you can still use combinations to represent permutations.
Permutations:
Distinctly ordered sets are called arrangements or permutations.
The number of permutations of n objects taken r at a time is given by:
where n = number of objects, r = number of positions
Special restrictions:
Eg. In how many ways can 5 boys and 4 girls be arranged on a bench if
a) there are no restrictions?
Solution : 9! or 9P9
b) boys and girls alternate?
Solution : A boy will be on each end
BGBGBGBGB= 5x4x4x3x3x2x2x1x1 = 5! x 4! or 5P5 x 4P4
Eg. In how many ways can 5 boys and 4 girls be arranged on a bench if
c) boys and girls are in separate groups?
Solution : Boys and Girls or Girls and Boys =5!x4!+4!x5!= 5!x4!x2
or 5P5 x 4P4 x 2
d) Anne and Jim wish to stay together?
Solution: (AJ)_ _ _ _ _ _ _ _ =2x8! or 2x8P8
Combination:
The number of different combinations (i.e. unordered sets) of r objects from n distinct objects is represented by :
No. of = (b number of permutations Combinations)/(arrangements of r objects)
