8 men entered a lounge simultaneously. If each person shook hands with the other, then find the total no. of hand shakes ?

This is a problem of combinations.

Step 1: Understand the problem In this problem, we are trying to find out how many handshakes would occur if each of the 8 men shook hands with each other once.

Step 2: Use the formula for combinations The formula for combinations is nCk = n! / [(n-k)! * k!], where n is the total number of items, k is the number of items to choose, and "!" denotes factorial.

Step 3: Apply the formula to the problem In this case, n = 8 (the total number of men) and k = 2 (since a handshake involves 2 people). So, we need to calculate 8C2 = 8! / [(8-2)! * 2!].

Step 4: Calculate the factorial values 8! = 87654321 = 40320 6! = 654321 = 720 2! = 2*1 = 2

Step 5: Substitute the factorial values into the formula 8C2 = 40320 / (720 * 2) = 40320 / 1440 = 28

So, if each of the 8 men shook hands with each other once, there would be a total of 28 handshakes.