Simply and counting

Question

Fifteen students are going hiking on their spring break they plan to travel in three vehicles one seating 7 one seating 5 one seating 3 students in how many ways can the students group themselves for thr trip

Answer 1

15! / (7!5!3!) =

 

15*14*13*12*11*10*9*8/ 5*4*3*2*3*2

 

14*13*12*11*10*9*8/4*2*3*2 <---- 15 cancels

 

14*13*2*11*10*9 <--- 8 cancels; 12 cancels

 

14*13*22*90

 

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