Permutations
A
permutation is an ordered arrangement of every or some elements of a set
of objects. Order is important in a permutation; therefore, permutations
with the same objects in a different order are considered distinct
arrangements.
For example if there are two objects A and B then the
different arrangements are, AB and BA, thus there are two ways in which A
and B can be arranged. A permutation of n distinct objects taken r at a
time is a subset, with r elements, of the n distinct objects. If there are
n distinct objects then the different possible arrangements taking r of
them is denoted as:
Examples
1. Six flights are scheduled
from city A to B and then back from B to A. In how many ways can a person
go to B from A and then return to A if he doesn't takes the same flight
for his return journey.
(A) 30
(B) 40
(C) 36
(D) 20
E) 24
Solution: The person can go from A to
B in six ways. For the return journey he cannot take the same flight thus
he can return in five ways. Therefore, the total number of ways = 6 × 5 =
30. Hence, (A)
2. In how many ways can a
committee of 4 be formed out of 8 people?
(A) 140
(B) 60
(C) 70
(D) 72
(E) 42
Solution: The numbers of ways in which
a committee of 4 can be selected out of 8 are:
Therefore:
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