There are 40 people at Drake's sweet sixteen party. Drake's only rule is that everyone in the party must meet and shake each others hand. If all 40 guest shake each other's hand once and only once. (1) How many handshakes are there altogether? (50 pts) (2) How did you get your solution? No verbiage should be the same for this. There are multiple ways to think about this. (30 pts) (3) What's the quickest way to figure this out if Drake invited 1000 people? (20 pts)

Explain

There are 780 handshakes.

1) This is a combination, so use ⁴⁰C₂.

⁴⁰C₂ = 780

There are 780 handshakes in total.

2) I got my solution by using the combinations formula. Or another way you could do this is to add up ... 39 + 38 + 37 + 36 + 35 + 34 + 33 + 32 + 31 ... + 1. You will end up with 780 (I did this to double check my work).

3) The quickest way to figure this out if Drake invited 1,000 people is to use the natural numbers formula = n (n + 1) / 2.

Plug the numbers in: 999 (1000) / 2 = 499,500

If Drake invited 1,000 people, there would be 499,500 handshakes.