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.
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.
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Suppose there are n people in the party. The first person shakes hand with the other (n-1) guests. The second guest shakes hand with the other (n-2) guests. this will continue until the (n-1) th guest shakes hand with the nth guest.
Total number of handshakes is (n-1) + (n-2).. + 3 + 2 + 1. .
= ((n-1)(n))/2 .
For example, 6 people in a party shake hand with other guests. So how many handshakes will be there?.
=((6-1)(6))/2.
=15.
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The quickest way to calculate percentages is to multiply numbers first and handle two decimal places later.
For example, 20% of 70 is 20 x 70 = 1400, so the answer is 14. .
70% of 20 is also 14.
To calculate the percentage of 72 or 29, then round up and down to the nearest multiple (70 and 30 respectively) to get a quick approx result.
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