Question

How many different batting orders are possible if 9 people are chosen from a group of 12 on a baseball team?

Answer 1

So we need to choose 9 people from the 12 persons.

Here the order of arrangement of the 9 persons is relevant.

So the answer is 12 Permutation 9 = ¹²P₉

¹²P₉ = (12!) / (12 - 9)! 
          
       =  (12!) / 3! 
 
       =  (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3!) / 3! 
 
       =  12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4

       =  79 833 600

      =  79 833 600 different orders