Question

No.of straight lines obtain by joining 16 points on a plane, no 3 being on the same line=?

Answer 1

The number of straight lines obtained by joining 16 points on a plane, no three of them being on the Same line is...

Ans: 120

Answer 2

Answer:

$Number \: of \: straight \: lines \: obtained \\by\: joining \: 16 \: points = \green {120}$

Step-by-step explanation:

$Number \: of \: points (n) = 16$

$Number \: of \: straight \: lines \: obtained \\by\: joining \: n \: points = ^{n}C_{2}$

$Number \: of \: straight \: lines \: obtained \\by\: joining \: 16 \: points = ^{16}C_{2}$

$\boxed { \pink { ^{n}C_{r} = \frac{n!}{(n-r)! r! }}}$

$= \frac{16!}{(16-2)! 2! }\\= \frac{16\times 15\times 14!}{14! 2}\\= \frac{16\times 15}{2}\\= \frac{240}{2} = 120$

Therefore.,

$Number \: of \: straight \: lines \: obtained \\by\: joining \: 16 \: points = \green {120}$

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