A group of 8 friends go to the movies. A bag of popcorn costs $2.99. How much will it cost to get one bag of popcorn for each fr
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Answer:
Given:
Total Number of people at the Drake’s sweet sixteen party = 40
Everyone in the party must meet and shake each other’s hand
1) How many handshakes are there altogether?
There was total of 780 handshakes in the party.
2. How did you get your solution:
If you have 7 people, person seven shakes six other hands, person
six shakes five other hands, person five shakes fours other hands,
person ,four shakes three other hands, person three shakes two other hands, and person two shakes one hand. Another way to see it is,
Person 7 +person 6 + person 5 + person 4 +person 3 + person 2 + person 1
= 6+5+ 4+3+2+1
=>21
so similairly in case of 40 persons
= 39+38+37+36+37+36+35+34 .................+3+2+1
=>780
3) What’s the quickest way to figure this out if Drake invited 1,000 people?
People at Party Number of Handshakes
2 1
3 1 + 2 = 3
4 1 + 2 + 3 = 6
5 1 + 2 + 3 + 4 = 10
6 1 + 2 + 3 + 4 + 5 = 15
.
.
.
n 1 + 2 + ...+ (n-1) = --------
Hence for n persons the number of handshakes will be
So for 1000 persons the number of handshakes will be
=>
=>
=>
=>499,500
Let 
be the identity matrix. Then pick whatever matrix you like for 
.