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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