Question

Six persons meet in a room and each shakes hands with all the others Find the total number of hand shakes that took place

• A. $15$
• B. $45$
• C. $12$
• D. $10$

Answer 1

The correct option is A $15$

Number of ways in which two people from $6$ people shake hand with each other is ${6_C}_2=\frac{6!}{2!(6-2)!}=\frac{6\times 5\times 4!}{2\times 4!}=15$
Here we applied the formula ${n_C}_r=\frac{n!}{r!(n-r)!}$