I do not understand how to solve this problem.

Question

Aliens with three heads, three arms and hands and three legs and feet, are visiting Earth. You observe how a group of 5 aliens greets each other. They seem to have to do everything in threes. A greeting consists of three aliens holding hands and touching their heads. How many greetings of this kind will there be in this group of 5 aliens, if a greeting among three aliens counts as one? An hour later, 1 more alien joins them and the greeting process starts all over again. How many greetings of this kind will there be in this group of 6 aliens?

Answer 1

(A) 5 choose 3 =

      5!/3!2!

=5*4/2= 10

 

(B) 6 choose 3=

       6!/3!3!=

       6*5*4/3!=20