Khamis, 7 Julai 2016
Permutation and Combination
Permutation : Permutation means arrangement of things. The word arrangement is used, if the order of things is considered.
Combination: Combination means selection of things. The word selection is used, when the order of things has no importance.
Distinctly
ordered sets are called arrangements or permutations.
Example :
A
flutter on the horses There are 7 horses
in a race.
a) In how many different orders can the horses
finish?
b) How many trifectas (1st , 2nd and 3rd) are
possible?
Solution
:
a) 7.6.5.4.3.2.1=7!
OR 7P7
b) 7.6.5
= 210 or 7P3
Permutations
with Restrictions
In how
many ways can 5 boys and 4 girls be arranged on a bench if there are
a) no
restrictions?
b) boys
and girls alternate?
c) Anne
and Jim wish to stay together?
Solution :
a) 9!
b) A boy
will be on each end BGBGBGBGB = 5.4.4.
3.3.2.2.1.1
Or 5! x
4! or 5P5x4P4
c) (AJ)
_ _ _ _ _ _ _ = 2.8! or 2.8P8
Arrangements
with Repetitions
How many
different arrangements of the word
PARRAMATTA are possible? Arrangements with Repetitions
P A R R
A M
A
TT
A
Solution
: 10 letters but note repetition (4 A’s, 2 R’s, 2 T’s)
No. of
arrangements = 10!/(4! 2! 2! ) = 37 800
Combination
The
number of different combinations (i.e. unordered sets)
No.of
combination = (number of permutations
)/( arrangements of r objects)
Example
:
How many
ways can a basketball team of 5 players be chosen from 8 players?
Solution
:
8C5
Example
2 :
A
committee of 5 people is to be chosen from a group of 6 men and 4 women. How
many committees are possible if
- there are no restrictions?
- one particular person must be chosen on the committee?
- one particular woman must be excluded from the committee?
Solution
:
- 10C5
- 1.9C4
- 9C5
Example
3:
In
a hand of poker, 5 cards are dealt from a regular pack of 52 cards.
In
how many of these hands are there:
All
hearts?
Solution
: 13C5
All the same colour?
Solution:
RED and BLACK
26C5
+ 26C5 = 2.26C5
:P I want you to answer my question
BalasPadamIn how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?? Explain please hehehe
In that case you need to select 5 men from 7 men and 2 women from 3 women.
PadamNumber of ways to do this
= 7C5 × 3C2
= 7C2 × 3C1 [∵ nCr = nC(n-r)]
=7×62×1×3=21×3=63