Twenty-four girls are trying out for 12 spots on the cheerleading team. if you want to determine how many different groups of 12 girls can be created

We are simply trying to select any 12 girls from the 24 girls.

Here the order in which the 12 girls are arranged does not matter.

So this is a combination problem.

So the answer is 24 combination 12.

24 Combination 12 =    24! / ((24 - 12!)12!)
        
                               =     24! / ( (12!)12!)
 
                     =  24*23* 22*21*20*19*18*17*16*25*14*13*12! / (12!12!) 
 
                     =  24*23* 22*21*20*19*18*17*16*25*14*13 / 12!
                          
Use a calculator.

                     = 2704156  different groups