Handshake Problem

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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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! . .


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:.

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. ....

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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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