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Answer to Q59

There are 120 people at a party and everyone shook hands. How many handshake will there be?

If you got Q34 right or atleast studied the answer, you should get this question right!

It is known that the number of handshake within a group of people is the sum of integer between 1 and (number of people in the group - 1). Say there are persons A, B, C, D and E (5 people) in a group and all shook hands, the number of handshakes will be sum of integers between 1 and (5-1) i.e. 1 + 2 + 3 + 4 = 10.

Let's confirm this:
- Person A shakes B, C, D, and E (4 handshakes)
- Person B shakes C, D, and E (no need to shake A again because A already shook him) (3 handshakes)
- Person C shakes D and E (2 handshakes)
- Person D shakes E (1 handshake)
- Person E don't have to shake anybody, they have all shook him

So, 4 + 3 + 2 + 1 = 10

And also we know that the sum of 1 to n = (n(n+1)) ÷ 2. Say you want to add 1 to 10 that will be
= (10 x (10 + 1)) ÷ 2
= (10 x 11) ÷ 2
= 110 ÷ 2
= 55 (also try it with your calculator)

With this information, we now know the number of handshakes in a group of 120 people will be 1 + 2 + 3 + ... + 119

But we don't have to add sequentially like that, we just do (119 x 120) ÷ 2
= 14280 ÷ 2
= 7140

Answer: 7140

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664 viewsSep 11, 2019 at 13:50

Answer to Q59

There are 120 people at a party and everyone shook hands. How many handshake will there be?

If you got Q34 right or atleast studied the answer, you should get this question right!

It is known that the number of handshake within a group of people is the sum of integer between 1 and (number of people in the group - 1). Say there are persons A, B, C, D and E (5 people) in a group and all shook hands, the number of handshakes will be sum of integers between 1 and (5-1) i.e. 1 + 2 + 3 + 4 = 10.

Let's confirm this:
- Person A shakes B, C, D, and E (4 handshakes)
- Person B shakes C, D, and E (no need to shake A again because A already shook him) (3 handshakes)
- Person C shakes D and E (2 handshakes)
- Person D shakes E (1 handshake)
- Person E don't have to shake anybody, they have all shook him

So, 4 + 3 + 2 + 1 = 10

And also we know that the sum of 1 to n = (n(n+1)) ÷ 2. Say you want to add 1 to 10 that will be
= (10 x (10 + 1)) ÷ 2
= (10 x 11) ÷ 2
= 110 ÷ 2
= 55 (also try it with your calculator)

With this information, we now know the number of handshakes in a group of 120 people will be 1 + 2 + 3 + ... + 119

But we don't have to add sequentially like that, we just do (119 x 120) ÷ 2
= 14280 ÷ 2
= 7140

Answer: 7140

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