B tech. Discrete mathematics (I. T & Comp. Science Engg.) Syllabus

PERMUTATIONS AND COMBINATIONS:

Permutation is the arrangement of objects with ordering, whereas combination is the selection of objects without ordering.

Permutation Formula:

1. The permutation of n – things taken r at a time without repetition is P(n, r) = n!/(n - r)!

n = the total number of items you have from which to take r = the number you are actually going to use.

2. 
   The permutation of n – things taken r at a time with repetition is P(n, r) = n^r
   
3. 
   The permutation of n – things taken all at a time with repetition is
   

P(n,n) = n!
Factorial Rule: For n items, there are n! (pronounced n factorial) ways to arrange them.

n! = (n)(n - 1)(n - 2). . . (3)(2)(1)

For example:

3! = (3)(2)(1) = 6

4! = (4)(3)(2)(1) = 24

5! = (5)(4)(3)(2)(1) = 120

6! = (6)(5)(4)(3)(2)(1) = 720