Combinations and Permutations
Combinations and Permutations
Permutation and combination related questions are common in PSC and Bank exams.
Before going to Combinations and Permutations, first lean about factorial.
If n is a positive integer then, factorial of n is denoted as n!.
5! = ( 1 x 2 x 3 x 4 x 5 ) = 120
4! = (1 x 2 x 3 x 4 ) = 24
Permutations are for lists of items, whose order matters and combinations are for group of items where order doesn’t matter. in other words,
- When the order of items doesn\\\'t matter, it is called as Combination.
- When the order of items does matter it is called as Permutation.
The number of permutations of n objects taken r at a time is determined by using this formula:
P(n,r)=n!/(n−r)!
Permutation: Listing your 3 favourite football team in order, from list of 10 teams. P(10,3) = 720.
The number of combinations of n objects taken r at a time is determined by using this formula:
C(n,r)=n!/((n−r)!r!)
Combination: Picking a team of 3 people from a football coaching group of 10. C(10,3) = 10!(3!(10−3)!) = 120.
കോൺവെക്സ് - ദീർഘദൃഷ്ടി.
കോൺകേവ് - ഹ്രസ്വദൃഷ്ടി .
സിലണ്ട്രിക്കൽ - വിഷമദൃഷ്ടി.
കോഡ്: .
മലയാളത്തിൽ \'\'കോൺവെക്സ് \" എന്നെഴുതുമ്പോൾ മറ്റ് ലെൻസുകളെ അപേക്ഷിച്ച് ദീർഘമുള്ള പേരാണ് ഇത്. അതിനാൽ ദീർഘദൃഷ്ടി പരിഹരിക്കാനുപയോഗിക്കുന്നു \' .
മലയാളത്തിലെഴുതുമ്പോൾ \"കോൺകേവ് \" എന്ന വാക്ക് മറ്റ് ലെൻസുകളുടെ പേരെഴുതുന്നതിനേക്കാൾ ചെറുതാണ്. ഹ്രസ്വദൃഷ്ടി പരിഹരിക്കാനുപ...
Problems Type 1: .
A can finish work in X days. .
B can finish work in Y days.
Both can finish in Z days = (X*Y) / (X+Y). .
Problems Type 2: .
Both A and B together can do work in T days.
A can do this work in X days.
then, B can do it in Y days = (X*T) / (X-T) .
Problems Type 3: .
A can finish work in X days.
B can finish work in Y days.
C can finish work in Z days.
Together they can do work in T days = (X*Y*Z)/ [(X*Y)+(Y*Z)+(X*Z)] .
Problems Type 4: .
A can finish work in X days.
B can finish work in Y days.
A*X = B*Y.
...
BODMAS is an acronym and it stands for Bracket, Of, Division, Multiplication, Addition and Subtraction. .
This explains the order of operations to solve an expression. According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve/simplify the bracket followed by of (powers and roots etc.), then division , multiplication , addition and subtraction from left to right. .
Example :.
7 + (6 × 52 + 3) = 7 + (6 × 25 + 3).
7 + (150 + 3).
7 + (153).
7 + 153 .
Ans: 160. .
...
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