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Summary Mind map for JEE Mathematics
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This is mind map for JEE aspirintts. This is for Permutation and combinations chapter of mathematics
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Permutation & combinati01 Fundamental Principles of - Cou
(1) Multiplication Principle (2) Addition Principle
If an operation can be performed In 'm' different way, following which a second operation If an operation can be performed in
can be performed in 'n' different ways, then the two operations in succession can be independent of the first operation, c
performed in m × n ways.This can be extended to any finite number of operations the two operations can be performe
finite number of mutually exclusive o
02 Permutation
03 Importan
01
Each of the different arrangements which can be made
Number of permutations of n different things, t
n!
by taking some or all of a number of things is called permutations. pr =
n
= n (n − 1)(
(n − r )!
Factorial notation: n! = n(n – 1) (n – 2)……3 × 2 × 1
Number of permutations of n different t
n! = n(n – 1)! 0! = 1! = 1
2n! = 2n × n! [1, 3, 5, 7 …….. (2n – 1)] P0 = 1, nP1 = n, nPn = n!
n n
Pr = n(n–1Pr–1) = n (n
Factorials of negative integers are not defined. Pn = n! n
Pr = n–1Pr
02 03
The number of permuation of n things Number of permutations
The number of permutations of
taken all at a time, p are alike of one kind, particular thing is to be a
n different things taken r at a time
Number of permutations
q are alike of seond kind r are alike of when each thing may be repeated
n! particular things is to be
a third kind and n=p+q+r ; any numbr of times is nr.
p!q!r! p! (r – (p – 1)) n–PPr–p
05 06
Number of permutations of n different Number of permutation
Number of permutation of n different things things, taken all at a time, when m
taken r at a time, when a particular things when m specified thing
specified things always come together
is never taken in each arrangement is n – 1Pr. is m! × (n – m + 1)! (n – m + 1)!
04
Arrangement round a circular table: Number of c
Circular Permutations taken all at a time is (n – 1)!, if clockwise & anticlo
Arrangement of beads around a circular necklace: Number of circular permutations of n different things taken
anticlockwise orders are taken as not different
Number of circular permutations of n different things taken r at a time is-
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