Summary Class 11 Maths JEE Brilliant Pala Notes - permutations and combinations

Lt-22 MATHEMATICS




PERMUTATION AND COMBINATION




I Fundamental Principles of Counting: Multiplication Principle (Multiplication Rule)
If an event can occur in ‘m’ different ways following which another event can occur in ‘n’ different ways,
then the total number of occurrence of the events in given order is m×n.
Multiplication principle can be extended to any number of events
Addition Principle (Addition Rule)
If an event can occur in ‘m’ different ways and an another event can occur in ‘n’ different ways, then the
total number of occurence of event one or event two can be in m+n difference ways
Addition principle can also be extended to any number of events
Note: ‘and’ represents multiplication and ‘or’ represents addition
II Factorial
Factorial of a natural number n in represented by n! or and in equal to the product of first ‘n’ natural
numbers
ie, n! = n(n–1) (n–2) (n–3)..3.2.1
Note:
1) 0! is defined as 1
2) n! = n(n–1)!=n(n–1)(n–2)! so on
III Permutation (Arrangement)
Result: The number of ways of arranging n distinct objects taken ‘r’ at a time without repetition is
denoted by nPr or P(n,r) and in equal to n. n  1 .  n  2  . n  3 ...(n  r  1)

n!
nPr  ,0  r  n
  r !
n

Note:
1) nP0=1
2) nPn=n!
3) nPn=nPn-1=n!
Result: Number of arrangements of n distinct objects taken ‘r’ at a time if repetition is allowed is nr


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