Question

if 30 students shakes each other then how many total shakes are?​

Answer 1

Answer:

15.....................

Answer 2

Shaking hands is meant to meet two persons or to simply join their hands, right? Here each student may have a shake hand with each other, but recommended that one can shake hand of another student at once, i.e., no repeated handshakes with the same student occur.

Shaking hands of two students is similar to combining two students, so here we can say that combination occurs among the students.

Thus the formula says that the minimum no. of shake hands among n students, provided one may meet all other only once, is equivalent to no. of ways of combining two students, i.e., it's nothing but nC2.

Here are 30 students, then the total number of shake hands among them is 30C2 = 30 × 29 / 2 = 435.

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