Please help explain these questions

Question

a. How many combinations are there of a set of n distinct objects taken r at a time?

b. How many combinations are there of six distinct objects taken three at a time?

Answer 1

(a).  n! = n(n-1)(n-2)(n-3)...(3)(2)(1)

 

         For example, 5! = (5)(4)(3)(2)(1) = 120

 

         The number of combinations of a set of n objects taken r at a               time = _nC_r

 

                   = n!/[r!(n-r)!]

 

(b).  ₆C₃ =6![3!(6-3)!] = 720/[(6)(6)] = 720/36 = 20