The probability 2 freshmen and 1 sophomore are selected is?

Question

Three people are selected from a group of 8 freshmen and 6 sophomores.

Answer 1

Calculate the probability 2 freshmen and 1 sophomore are selected :

n (A)          = 8C₂*6C₁

                 = ( 8!/ (8 -2)! 2!) *( 6!/ (6 -1)! 1!)

                 = ( (8*7) 6!/ 6! 2*1) *( 6*5!/ 5! 1)

                 = ( (8*7)/ 2) *(6)  

                  = 28*6

                 = 168

n (s) = 14C₃  = 364

P (A) = n (A)/n (s)

         = 168/364

         = 0.4615