C(9,6) how to solve

Question

combinations in math for liberal arts,

 

C(9,6)

Answer 1

C(9,6) means 9 objects taken 6 at a time

how many combinations are there ?

use the formula n!/r!(n-r)! where n=9 and r=6

9!/6!(9-6)!

9!/6!(3)!

(9*8*7*6*5*4*3*2*1)/(6*5*4*3*2*1)(3*2*1)

simplify

(9*8*7)/(3*2*1)

simplify again (9/3=3 and 8/2=4)

3*4*7=84