Question

the seven supreme court justices have a hand shaking ritual that they conduct just before each session. each of the justices shake hands with every other justice. how many handshakes will there be in this ritual??

Answer 1

yep

Answer 2

oh okay thankyou so much. that's what i was about to do.

Answer 3

No, that answer is wrong. That is the answer to a question such as "How many unique ways can the 7 justices sit left to right on the bench?"

Imagine the seven lined up by seniority. The first justice then goes down the line and has to shake 6 hands; the second justice then goes down and shakes 5 hands; the third justice 4 hands; etc.

So the total is 6 + 5 + 4 + 3 + 2 + 1 = 21.

Answer 4

That's a great way of thinking through the problem

Answer 5

By the way, if you just sense check the first answer you can see it couldn't possibly be right.

Suppose each hand shake took 3 seconds. Then 7.6.5.4.3.2 * 3 seconds = 15,120 seconds or more than 4 hours.

Answer 6

ohh i understand now. oh and this problem has nothing to do with the formula nCr right? and thankyou

Answer 7

yes, I totally misread the problem.