Kenneth S. answered • 05/09/16
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This is usually stated, more carefully, as ten people, all previously strangers, meet in a room; each person shakes hands with every other person, once. How many handshakes were there?
If not expressed carefully, one is tempted to answer your question as 20 (assuming no amputees). But this is probably intended to be a Combinations Problem, 10C2 being a likely answer.
Kenneth S.
The answer is 45 because the value of 10C2 is 45, according to the formula 10!/[2!8!] which is 10(9)/2.
The MEANING of nCr is "from n objects (persons, in this case), how many distinct combinations are there involving r selected at a time."
It's reasonable to have assumed that this Combinations formula (and a related Permutations formula) were known to any student to whom a question of this type were posed. It's a combinatorics type of question and one prepares students for such questions by discussions involving nCr and nPr formulae.
DO re-read, carefully, the manner in which I correctly restated the question, and DO share this whole discussion with your teacher.
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05/09/16
Kristin B.
05/09/16