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So, There is this question which I came across. "Total no of handshakes among 15 people." The answer seems to be just 15C2. Isn't that just a way of selecting and not the number of handshakes? I'm in grade 10th. So don't judge.

PrincessEev
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Jaimeblt1
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2 Answers2

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$_{15}C_2$ is the number of ways to select 2 people from 15 people (when order doesn't matter). This is exactly the number of handshakes that occur if $15$ people all shake hands with each other. There is one handshake for each set of 2 people.

littleO
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I mean, $_{15}C_2$ gives a numerical result as well even if describes a method of selection:

$$_{15}C_2 = \frac{15!}{2! \cdot (15-2)!}$$

and generally

$$_{n}C_r = \frac{n!}{r! \cdot (n-r)!}$$

Do the calculations and boom, a number. $_{n}C_r$ is just a notation representing the underlying number (or, rather, the calculations leading up to that number), because who wants to write that fraction every single time?

PrincessEev
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  • I'm not quite sure. 15C2 in literal terms means, you select 2 objects out of 15. Nowhere does it say that selection is equal to the number of handshakes. Pardon if i'm missing something obvious. – Jaimeblt1 Dec 16 '18 at 08:33
  • What are you unsure about? – PrincessEev Dec 16 '18 at 08:34
  • Check it out. I edited it. – Jaimeblt1 Dec 16 '18 at 08:39
  • No, $_{15}C_2$ represents the number of ways in which you can choose $2$ objects from $15$. It does not mean "choose a single pair of $2$ from $15$" - it means the number of ways in whichiyou can choose those pairs. I guess, yes, you could argue that in the sense of languages and the usual connotation in English it means to choose $2$ from $15$, but if you go on to study math one day in more depth you'll realize that the mathematical meaning and the common/everyday meaning may differ greatly. – PrincessEev Dec 16 '18 at 08:43
  • Mathematicians make very poor poets, so to speak, and can suck at developing intuitive, not-confusing notations/conventions for various things. But either way, that's just how mathematical notation and standards have developed. – PrincessEev Dec 16 '18 at 08:43
  • I get it now. Thank you. – Jaimeblt1 Dec 16 '18 at 08:47