Question

23 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence

Answer 1

Each person will handshake with rest others
Here, all 23 persons will handshake with other 22 persons.
Hence, total no of handshake should be 22×23
But , Handshake of 1st person with 2nd is same as 2nd with 1st.
So, we will divide result/2
Total handshakes in cyclic sequence = $\frac{22 * 23}{2}$
                                                           = 11×23
                                                           = 253

Answer 2

Step-by-step explanation:

N people then arrange in cyclic way.

Possibility = n - 1

Here,

23 people then possible is (23-1)>=22.