Question
Download Solution PDFThere are 40 people in a group. If they shake hands with one another, how many handshakes are possible?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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
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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