Question

The number of hand shake in 30 persons.​

Answer 1

Answer:

435

Step-by-step explanation:

no of handshake = C(30,2) = 30!/(2!28!) = 435

Answer 2

$We \: use \: combination \: formula :$

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

$Where, \: n = Total \: number \: of \: persons \\r = number \: of \: handshakes \\Here, \: n = 30, \\r = 2$

$Applying \:the \: formula$

$Total \: number \: of \: hand \: shakes \\= \frac{30!}{(30-2)! 2!}\\= \frac{30!}{28! 2!}\\= \frac{30\times 29 \times 28! }{28! 2}\\= \frac{30\times 29 }{2} \\= 15 \times 29 \\= 435$

Therefore.,

$\red {Total \: number \: of \: hand \: shakes} \green {= 435}$

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