SOLUTION: You volunteer to drive children at a charity event to the zoo but only 6 out of the 19 children can fit in your van. How many combinations of 6 from the 19 can you take?

Algebra ->  Permutations -> SOLUTION: You volunteer to drive children at a charity event to the zoo but only 6 out of the 19 children can fit in your van. How many combinations of 6 from the 19 can you take?      Log On


   

Question 984244: You volunteer to drive children at a charity event to the zoo but only 6 out of the 19 children can fit in your van. How many combinations of 6 from the 19 can you take?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use the combination formula

n C r = (n!)/(r!(n-r)!)

19 C 6 = (19!)/(6!*(19-6)!)

19 C 6 = (19!)/(6!*13!)

19 C 6 = (19*18*17*16*15*14*13!)/(6!*13!)

19 C 6 = (19*18*17*16*15*14)/(6!)

19 C 6 = (19*18*17*16*15*14)/(6*5*4*3*2*1)

19 C 6 = (19535040)/(720)

19 C 6 = 27132

-------------------------------------------------------

There are 27,132 different combinations.