There are 40 people in a group. If they shake hands with one another, how many handshakes are possible?

This question was previously asked in
TSPSC Group 4 Secretarial Ability Official Paper-II (Held in: 2018)
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  1. 880
  2. 390
  3. 800
  4. 780

Answer (Detailed Solution Below)

Option 4 : 780
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TSPSC Group 4 CT 1: General Studies(International Relations and Events)
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Detailed Solution

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Given:

Number of people = 40

Formula used:

nCr = n!/(r!(n – r)!)

Calculation:

n = 40

r = 2

40C2 = 40!/(2!(40 – 2)!) = (40 × 39)/2

⇒ 780 

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Each person (in the group of 40) shakes hands with all others (other 39 members). 

So, total number of handshakes = 40 × 39 = 1560

But, when one is shaking hands with another, we can say, the other is also shaking hands with the first one.

For example, when A shakes hands with B, it means that B is shaking hands with A.

That means, here, we have considers in the 1560 handshakes, two people shaking hands twice.

So, the total number of handshakes = 1560/2 = 780 handshakes.

∴ The possible number of handshakes is 780.

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